Tablas Estadisticas

X ∼ B(n, p) P (X ≤ x)
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.9900 0.9800 0.9700 0.9600 0.9500 0.9400 0.9300 0.9200 0.9100 0.9000 0.8900 0.8800 0.8700 0.8600 0.8500 0.8400 0.8300 0.8200 0.8100 0.8000 0.7900 0.7800 0.7700 0.7600 0.7500
1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
n=1
0 0.7400 0.7300 0.7200 0.7100 0.7000 0.6900 0.6800 0.6700 0.6600 0.6500 0.6400 0.6300 0.6200 0.6100 0.6000 0.5900 0.5800 0.5700 0.5600 0.5500 0.5400 0.5300 0.5200 0.5100 0.5000
1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.9801 0.9604 0.9409 0.9216 0.9025 0.8836 0.8649 0.8464 0.8281 0.8100 0.7921 0.7744 0.7569 0.7396 0.7225 0.7056 0.6889 0.6724 0.6561 0.6400 0.6241 0.6084 0.5929 0.5776 0.5625
1 0.9999 0.9996 0.9991 0.9984 0.9975 0.9964 0.9951 0.9936 0.9919 0.9900 0.9879 0.9856 0.9831 0.9804 0.9775 0.9744 0.9711 0.9676 0.9639 0.9600 0.9559 0.9516 0.9471 0.9424 0.9375
2 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
n=2
0 0.5476 0.5329 0.5184 0.5041 0.4900 0.4761 0.4624 0.4489 0.4356 0.4225 0.4096 0.3969 0.3844 0.3721 0.3600 0.3481 0.3364 0.3249 0.3136 0.3025 0.2916 0.2809 0.2704 0.2601 0.2500
1 0.9324 0.9271 0.9216 0.9159 0.9100 0.9039 0.8976 0.8911 0.8844 0.8775 0.8704 0.8631 0.8556 0.8479 0.8400 0.8319 0.8236 0.8151 0.8064 0.7975 0.7884 0.7791 0.7696 0.7599 0.7500
2 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.9703 0.9412 0.9127 0.8847 0.8574 0.8306 0.8044 0.7787 0.7536 0.7290 0.7050 0.6815 0.6585 0.6361 0.6141 0.5927 0.5718 0.5514 0.5314 0.5120 0.4930 0.4746 0.4565 0.4390 0.4219
1 0.9997 0.9988 0.9974 0.9953 0.9928 0.9896 0.9860 0.9818 0.9772 0.9720 0.9664 0.9603 0.9537 0.9467 0.9393 0.9314 0.9231 0.9145 0.9054 0.8960 0.8862 0.8761 0.8656 0.8548 0.8438
2 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9995 0.9993 0.9990 0.9987 0.9983 0.9978 0.9973 0.9966 0.9959 0.9951 0.9942 0.9931 0.9920 0.9907 0.9894 0.9878 0.9862 0.9844
3 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
n=3
0 0.4052 0.3890 0.3732 0.3579 0.3430 0.3285 0.3144 0.3008 0.2875 0.2746 0.2621 0.2500 0.2383 0.2270 0.2160 0.2054 0.1951 0.1852 0.1756 0.1664 0.1575 0.1489 0.1406 0.1327 0.1250
1 0.8324 0.8207 0.8087 0.7965 0.7840 0.7713 0.7583 0.7452 0.7318 0.7183 0.7045 0.6906 0.6765 0.6623 0.6480 0.6335 0.6190 0.6043 0.5896 0.5748 0.5599 0.5449 0.5300 0.5150 0.5000
2 0.9824 0.9803 0.9780 0.9756 0.9730 0.9702 0.9672 0.9641 0.9607 0.9571 0.9533 0.9493 0.9451 0.9407 0.9360 0.9311 0.9259 0.9205 0.9148 0.9089 0.9027 0.8962 0.8894 0.8824 0.8750
3 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.9606 0.9224 0.8853 0.8493 0.8145 0.7807 0.7481 0.7164 0.6857 0.6561 0.6274 0.5997 0.5729 0.5470 0.5220 0.4979 0.4746 0.4521 0.4305 0.4096 0.3895 0.3702 0.3515 0.3336 0.3164
1 0.9994 0.9977 0.9948 0.9909 0.9860 0.9801 0.9733 0.9656 0.9570 0.9477 0.9376 0.9268 0.9153 0.9032 0.8905 0.8772 0.8634 0.8491 0.8344 0.8192 0.8037 0.7878 0.7715 0.7550 0.7383
2 1.0000 1.0000 0.9999 0.9998 0.9995 0.9992 0.9987 0.9981 0.9973 0.9963 0.9951 0.9937 0.9921 0.9902 0.9880 0.9856 0.9829 0.9798 0.9765 0.9728 0.9688 0.9644 0.9597 0.9547 0.9492
3 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9995 0.9993 0.9992 0.9990 0.9987 0.9984 0.9981 0.9977 0.9972 0.9967 0.9961
4 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
n=4
0 0.2999 0.2840 0.2687 0.2541 0.2401 0.2267 0.2138 0.2015 0.1897 0.1785 0.1678 0.1575 0.1478 0.1385 0.1296 0.1212 0.1132 0.1056 0.0983 0.0915 0.0850 0.0789 0.0731 0.0677 0.0625
1 0.7213 0.7041 0.6868 0.6693 0.6517 0.6340 0.6163 0.5985 0.5807 0.5630 0.5453 0.5276 0.5100 0.4925 0.4752 0.4580 0.4410 0.4241 0.4074 0.3910 0.3748 0.3588 0.3431 0.3276 0.3125
2 0.9434 0.9372 0.9306 0.9237 0.9163 0.9085 0.9004 0.8918 0.8829 0.8735 0.8638 0.8536 0.8431 0.8321 0.8208 0.8091 0.7970 0.7845 0.7717 0.7585 0.7450 0.7311 0.7169 0.7023 0.6875
3 0.9954 0.9947 0.9939 0.9929 0.9919 0.9908 0.9895 0.9881 0.9866 0.9850 0.9832 0.9813 0.9791 0.9769 0.9744 0.9717 0.9689 0.9658 0.9625 0.9590 0.9552 0.9512 0.9469 0.9424 0.9375
4 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.9510 0.9039 0.8587 0.8154 0.7738 0.7339 0.6957 0.6591 0.6240 0.5905 0.5584 0.5277 0.4984 0.4704 0.4437 0.4182 0.3939 0.3707 0.3487 0.3277 0.3077 0.2887 0.2707 0.2536 0.2373
1 0.9990 0.9962 0.9915 0.9852 0.9774 0.9681 0.9575 0.9456 0.9326 0.9185 0.9035 0.8875 0.8708 0.8533 0.8352 0.8165 0.7973 0.7776 0.7576 0.7373 0.7167 0.6959 0.6749 0.6539 0.6328
2 1.0000 0.9999 0.9997 0.9994 0.9988 0.9980 0.9969 0.9955 0.9937 0.9914 0.9888 0.9857 0.9821 0.9780 0.9734 0.9682 0.9625 0.9563 0.9495 0.9421 0.9341 0.9256 0.9164 0.9067 0.8965
3 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9995 0.9993 0.9991 0.9987 0.9983 0.9978 0.9971 0.9964 0.9955 0.9945 0.9933 0.9919 0.9903 0.9886 0.9866 0.9844
4 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9995 0.9994 0.9992 0.9990
5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
n=5
0 0.2219 0.2073 0.1935 0.1804 0.1681 0.1564 0.1454 0.1350 0.1252 0.1160 0.1074 0.0992 0.0916 0.0845 0.0778 0.0715 0.0656 0.0602 0.0551 0.0503 0.0459 0.0418 0.0380 0.0345 0.0313
1 0.6117 0.5907 0.5697 0.5489 0.5282 0.5077 0.4875 0.4675 0.4478 0.4284 0.4094 0.3907 0.3724 0.3545 0.3370 0.3199 0.3033 0.2871 0.2714 0.2562 0.2415 0.2272 0.2135 0.2002 0.1875
2 0.8857 0.8743 0.8624 0.8499 0.8369 0.8234 0.8095 0.7950 0.7801 0.7648 0.7491 0.7330 0.7165 0.6997 0.6826 0.6651 0.6475 0.6295 0.6114 0.5931 0.5747 0.5561 0.5375 0.5187 0.5000
3 0.9819 0.9792 0.9762 0.9728 0.9692 0.9653 0.9610 0.9564 0.9514 0.9460 0.9402 0.9340 0.9274 0.9204 0.9130 0.9051 0.8967 0.8879 0.8786 0.8688 0.8585 0.8478 0.8365 0.8248 0.8125
4 0.9988 0.9986 0.9983 0.9979 0.9976 0.9971 0.9966 0.9961 0.9955 0.9947 0.9940 0.9931 0.9921 0.9910 0.9898 0.9884 0.9869 0.9853 0.9835 0.9815 0.9794 0.9771 0.9745 0.9718 0.9688
5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
X ∼ B(n, p) P (X ≤ x)
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.9415 0.8858 0.8330 0.7828 0.7351 0.6899 0.6470 0.6064 0.5679 0.5314 0.4970 0.4644 0.4336 0.4046 0.3771 0.3513 0.3269 0.3040 0.2824 0.2621 0.2431 0.2252 0.2084 0.1927 0.1780
1 0.9985 0.9943 0.9875 0.9784 0.9672 0.9541 0.9392 0.9227 0.9048 0.8857 0.8655 0.8444 0.8224 0.7997 0.7765 0.7528 0.7287 0.7044 0.6799 0.6554 0.6308 0.6063 0.5820 0.5578 0.5339
2 1.0000 0.9998 0.9995 0.9988 0.9978 0.9962 0.9942 0.9915 0.9882 0.9842 0.9794 0.9739 0.9676 0.9605 0.9527 0.9440 0.9345 0.9241 0.9130 0.9011 0.8885 0.8750 0.8609 0.8461 0.8306
3 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9995 0.9992 0.9987 0.9982 0.9975 0.9966 0.9955 0.9941 0.9925 0.9906 0.9884 0.9859 0.9830 0.9798 0.9761 0.9720 0.9674 0.9624
4 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9995 0.9993 0.9990 0.9987 0.9984 0.9980 0.9975 0.9969 0.9962 0.9954
5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998
6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
n=6
0 0.1642 0.1513 0.1393 0.1281 0.1176 0.1079 0.0989 0.0905 0.0827 0.0754 0.0687 0.0625 0.0568 0.0515 0.0467 0.0422 0.0381 0.0343 0.0308 0.0277 0.0248 0.0222 0.0198 0.0176 0.0156
1 0.5104 0.4872 0.4644 0.4420 0.4202 0.3988 0.3780 0.3578 0.3381 0.3191 0.3006 0.2828 0.2657 0.2492 0.2333 0.2181 0.2035 0.1895 0.1762 0.1636 0.1515 0.1401 0.1293 0.1190 0.1094
2 0.8144 0.7977 0.7804 0.7626 0.7443 0.7256 0.7064 0.6870 0.6672 0.6471 0.6268 0.6063 0.5857 0.5650 0.5443 0.5236 0.5029 0.4823 0.4618 0.4415 0.4214 0.4015 0.3820 0.3627 0.3438
3 0.9569 0.9508 0.9443 0.9372 0.9295 0.9213 0.9125 0.9031 0.8931 0.8826 0.8714 0.8596 0.8473 0.8343 0.8208 0.8067 0.7920 0.7768 0.7610 0.7447 0.7279 0.7107 0.6930 0.6748 0.6563
4 0.9944 0.9933 0.9921 0.9907 0.9891 0.9873 0.9852 0.9830 0.9805 0.9777 0.9746 0.9712 0.9675 0.9635 0.9590 0.9542 0.9490 0.9434 0.9373 0.9308 0.9238 0.9163 0.9083 0.8997 0.8906
5 0.9997 0.9996 0.9995 0.9994 0.9993 0.9991 0.9989 0.9987 0.9985 0.9982 0.9978 0.9974 0.9970 0.9965 0.9959 0.9952 0.9945 0.9937 0.9927 0.9917 0.9905 0.9892 0.9878 0.9862 0.9844
6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.9321 0.8681 0.8080 0.7514 0.6983 0.6485 0.6017 0.5578 0.5168 0.4783 0.4423 0.4087 0.3773 0.3479 0.3206 0.2951 0.2714 0.2493 0.2288 0.2097 0.1920 0.1757 0.1605 0.1465 0.1335
1 0.9980 0.9921 0.9829 0.9706 0.9556 0.9382 0.9187 0.8974 0.8745 0.8503 0.8250 0.7988 0.7719 0.7444 0.7166 0.6885 0.6604 0.6323 0.6044 0.5767 0.5494 0.5225 0.4960 0.4702 0.4449
2 1.0000 0.9997 0.9991 0.9980 0.9962 0.9937 0.9903 0.9860 0.9807 0.9743 0.9669 0.9584 0.9487 0.9380 0.9262 0.9134 0.8995 0.8846 0.8687 0.8520 0.8343 0.8159 0.7967 0.7769 0.7564
3 1.0000 1.0000 1.0000 0.9999 0.9998 0.9996 0.9993 0.9988 0.9982 0.9973 0.9961 0.9946 0.9928 0.9906 0.9879 0.9847 0.9811 0.9769 0.9721 0.9667 0.9606 0.9539 0.9464 0.9383 0.9294
4 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994 0.9991 0.9988 0.9983 0.9978 0.9971 0.9963 0.9953 0.9942 0.9928 0.9912 0.9893 0.9871
5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9995 0.9994 0.9992 0.9989 0.9987
6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999
7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
n=7
0 0.1215 0.1105 0.1003 0.0910 0.0824 0.0745 0.0672 0.0606 0.0546 0.0490 0.0440 0.0394 0.0352 0.0314 0.0280 0.0249 0.0221 0.0195 0.0173 0.0152 0.0134 0.0117 0.0103 0.0090 0.0078
1 0.4204 0.3965 0.3734 0.3510 0.3294 0.3086 0.2887 0.2696 0.2513 0.2338 0.2172 0.2013 0.1863 0.1721 0.1586 0.1459 0.1340 0.1228 0.1123 0.1024 0.0932 0.0847 0.0767 0.0693 0.0625
2 0.7354 0.7139 0.6919 0.6696 0.6471 0.6243 0.6013 0.5783 0.5553 0.5323 0.5094 0.4866 0.4641 0.4419 0.4199 0.3983 0.3771 0.3564 0.3362 0.3164 0.2973 0.2787 0.2607 0.2433 0.2266
3 0.9198 0.9095 0.8984 0.8866 0.8740 0.8606 0.8466 0.8318 0.8163 0.8002 0.7833 0.7659 0.7479 0.7293 0.7102 0.6906 0.6706 0.6502 0.6294 0.6083 0.5869 0.5654 0.5437 0.5219 0.5000
4 0.9847 0.9819 0.9787 0.9752 0.9712 0.9668 0.9620 0.9566 0.9508 0.9444 0.9375 0.9299 0.9218 0.9131 0.9037 0.8937 0.8831 0.8718 0.8598 0.8471 0.8337 0.8197 0.8049 0.7895 0.7734
5 0.9983 0.9979 0.9974 0.9969 0.9962 0.9954 0.9945 0.9935 0.9923 0.9910 0.9895 0.9877 0.9858 0.9836 0.9812 0.9784 0.9754 0.9721 0.9684 0.9643 0.9598 0.9549 0.9496 0.9438 0.9375
6 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9997 0.9996 0.9995 0.9994 0.9992 0.9991 0.9989 0.9986 0.9984 0.9981 0.9977 0.9973 0.9968 0.9963 0.9956 0.9949 0.9941 0.9932 0.9922
7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.9227 0.8508 0.7837 0.7214 0.6634 0.6096 0.5596 0.5132 0.4703 0.4305 0.3937 0.3596 0.3282 0.2992 0.2725 0.2479 0.2252 0.2044 0.1853 0.1678 0.1517 0.1370 0.1236 0.1113 0.1001
1 0.9973 0.9897 0.9777 0.9619 0.9428 0.9208 0.8965 0.8702 0.8423 0.8131 0.7829 0.7520 0.7206 0.6889 0.6572 0.6256 0.5943 0.5634 0.5330 0.5033 0.4743 0.4462 0.4189 0.3925 0.3671
2 0.9999 0.9996 0.9987 0.9969 0.9942 0.9904 0.9853 0.9789 0.9711 0.9619 0.9513 0.9392 0.9257 0.9109 0.8948 0.8774 0.8588 0.8392 0.8185 0.7969 0.7745 0.7514 0.7276 0.7033 0.6785
3 1.0000 1.0000 0.9999 0.9998 0.9996 0.9993 0.9987 0.9978 0.9966 0.9950 0.9929 0.9903 0.9871 0.9832 0.9786 0.9733 0.9672 0.9603 0.9524 0.9437 0.9341 0.9235 0.9120 0.8996 0.8862
4 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9997 0.9996 0.9993 0.9990 0.9985 0.9979 0.9971 0.9962 0.9950 0.9935 0.9917 0.9896 0.9871 0.9842 0.9809 0.9770 0.9727
5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9998 0.9997 0.9995 0.9993 0.9991 0.9988 0.9984 0.9979 0.9973 0.9966 0.9958
6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996
7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
n=8
0 0.0899 0.0806 0.0722 0.0646 0.0576 0.0514 0.0457 0.0406 0.0360 0.0319 0.0281 0.0248 0.0218 0.0192 0.0168 0.0147 0.0128 0.0111 0.0097 0.0084 0.0072 0.0062 0.0053 0.0046 0.0039
1 0.3427 0.3193 0.2969 0.2756 0.2553 0.2360 0.2178 0.2006 0.1844 0.1691 0.1548 0.1414 0.1289 0.1172 0.1064 0.0963 0.0870 0.0784 0.0705 0.0632 0.0565 0.0504 0.0448 0.0398 0.0352
2 0.6535 0.6282 0.6027 0.5772 0.5518 0.5264 0.5013 0.4764 0.4519 0.4278 0.4042 0.3811 0.3585 0.3366 0.3154 0.2948 0.2750 0.2560 0.2376 0.2201 0.2034 0.1875 0.1724 0.1581 0.1445
3 0.8719 0.8567 0.8406 0.8237 0.8059 0.7874 0.7681 0.7481 0.7276 0.7064 0.6847 0.6626 0.6401 0.6172 0.5941 0.5708 0.5473 0.5238 0.5004 0.4770 0.4537 0.4306 0.4078 0.3854 0.3633
4 0.9678 0.9623 0.9562 0.9495 0.9420 0.9339 0.9250 0.9154 0.9051 0.8939 0.8820 0.8693 0.8557 0.8414 0.8263 0.8105 0.7938 0.7765 0.7584 0.7396 0.7202 0.7001 0.6795 0.6584 0.6367
5 0.9948 0.9936 0.9922 0.9906 0.9887 0.9866 0.9841 0.9813 0.9782 0.9747 0.9707 0.9664 0.9615 0.9561 0.9502 0.9437 0.9366 0.9289 0.9206 0.9115 0.9018 0.8914 0.8802 0.8682 0.8555
6 0.9995 0.9994 0.9992 0.9990 0.9987 0.9984 0.9980 0.9976 0.9970 0.9964 0.9957 0.9949 0.9939 0.9928 0.9915 0.9900 0.9883 0.9864 0.9843 0.9819 0.9792 0.9761 0.9728 0.9690 0.9648
7 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9996 0.9995 0.9993 0.9992 0.9990 0.9988 0.9986 0.9983 0.9980 0.9976 0.9972 0.9967 0.9961
8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
X ∼ B(n, p) P (X ≤ x)
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.9135 0.8337 0.7602 0.6925 0.6302 0.5730 0.5204 0.4722 0.4279 0.3874 0.3504 0.3165 0.2855 0.2573 0.2316 0.2082 0.1869 0.1676 0.1501 0.1342 0.1199 0.1069 0.0952 0.0846 0.0751
1 0.9966 0.9869 0.9718 0.9522 0.9288 0.9022 0.8729 0.8417 0.8088 0.7748 0.7401 0.7049 0.6696 0.6343 0.5995 0.5652 0.5315 0.4988 0.4670 0.4362 0.4066 0.3782 0.3509 0.3250 0.3003
2 0.9999 0.9994 0.9980 0.9955 0.9916 0.9862 0.9791 0.9702 0.9595 0.9470 0.9328 0.9167 0.8991 0.8798 0.8591 0.8371 0.8139 0.7895 0.7643 0.7382 0.7115 0.6842 0.6566 0.6287 0.6007
3 1.0000 1.0000 0.9999 0.9997 0.9994 0.9987 0.9977 0.9963 0.9943 0.9917 0.9883 0.9842 0.9791 0.9731 0.9661 0.9580 0.9488 0.9385 0.9270 0.9144 0.9006 0.8856 0.8696 0.8525 0.8343
4 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9995 0.9991 0.9986 0.9979 0.9970 0.9959 0.9944 0.9925 0.9902 0.9875 0.9842 0.9804 0.9760 0.9709 0.9650 0.9584 0.9511
5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994 0.9991 0.9987 0.9983 0.9977 0.9969 0.9960 0.9949 0.9935 0.9919 0.9900
6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9994 0.9992 0.9990 0.9987
7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999
8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
n=9
0 0.0665 0.0589 0.0520 0.0458 0.0404 0.0355 0.0311 0.0272 0.0238 0.0207 0.0180 0.0156 0.0135 0.0117 0.0101 0.0087 0.0074 0.0064 0.0054 0.0046 0.0039 0.0033 0.0028 0.0023 0.0020
1 0.2770 0.2548 0.2340 0.2144 0.1960 0.1788 0.1628 0.1478 0.1339 0.1211 0.1092 0.0983 0.0882 0.0790 0.0705 0.0628 0.0558 0.0495 0.0437 0.0385 0.0338 0.0296 0.0259 0.0225 0.0195
2 0.5727 0.5448 0.5171 0.4898 0.4628 0.4364 0.4106 0.3854 0.3610 0.3373 0.3144 0.2924 0.2713 0.2511 0.2318 0.2134 0.1961 0.1796 0.1641 0.1495 0.1358 0.1231 0.1111 0.1001 0.0898
3 0.8151 0.7950 0.7740 0.7522 0.7297 0.7065 0.6827 0.6585 0.6338 0.6089 0.5837 0.5584 0.5331 0.5078 0.4826 0.4576 0.4330 0.4087 0.3848 0.3614 0.3386 0.3164 0.2948 0.2740 0.2539
4 0.9429 0.9338 0.9238 0.9130 0.9012 0.8885 0.8748 0.8602 0.8447 0.8283 0.8110 0.7928 0.7738 0.7540 0.7334 0.7122 0.6903 0.6678 0.6449 0.6214 0.5976 0.5735 0.5491 0.5246 0.5000
5 0.9878 0.9851 0.9821 0.9787 0.9747 0.9702 0.9652 0.9596 0.9533 0.9464 0.9388 0.9304 0.9213 0.9114 0.9006 0.8891 0.8767 0.8634 0.8492 0.8342 0.8183 0.8015 0.7839 0.7654 0.7461
6 0.9983 0.9978 0.9972 0.9965 0.9957 0.9947 0.9936 0.9922 0.9906 0.9888 0.9867 0.9843 0.9816 0.9785 0.9750 0.9710 0.9666 0.9617 0.9563 0.9502 0.9436 0.9363 0.9283 0.9196 0.9102
7 0.9999 0.9998 0.9997 0.9997 0.9996 0.9994 0.9993 0.9991 0.9989 0.9986 0.9983 0.9979 0.9974 0.9969 0.9962 0.9954 0.9945 0.9935 0.9923 0.9909 0.9893 0.9875 0.9855 0.9831 0.9805
8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9997 0.9996 0.9995 0.9994 0.9992 0.9991 0.9989 0.9986 0.9984 0.9980
9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.9044 0.8171 0.7374 0.6648 0.5987 0.5386 0.4840 0.4344 0.3894 0.3487 0.3118 0.2785 0.2484 0.2213 0.1969 0.1749 0.1552 0.1374 0.1216 0.1074 0.0947 0.0834 0.0733 0.0643 0.0563
1 0.9957 0.9838 0.9655 0.9418 0.9139 0.8824 0.8483 0.8121 0.7746 0.7361 0.6972 0.6583 0.6196 0.5816 0.5443 0.5080 0.4730 0.4392 0.4068 0.3758 0.3464 0.3185 0.2921 0.2673 0.2440
2 0.9999 0.9991 0.9972 0.9938 0.9885 0.9812 0.9717 0.9599 0.9460 0.9298 0.9116 0.8913 0.8692 0.8455 0.8202 0.7936 0.7659 0.7372 0.7078 0.6778 0.6474 0.6169 0.5863 0.5558 0.5256
3 1.0000 1.0000 0.9999 0.9996 0.9990 0.9980 0.9964 0.9942 0.9912 0.9872 0.9822 0.9761 0.9687 0.9600 0.9500 0.9386 0.9259 0.9117 0.8961 0.8791 0.8609 0.8413 0.8206 0.7988 0.7759
4 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9994 0.9990 0.9984 0.9975 0.9963 0.9947 0.9927 0.9901 0.9870 0.9832 0.9787 0.9734 0.9672 0.9601 0.9521 0.9431 0.9330 0.9219
5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9997 0.9996 0.9994 0.9990 0.9986 0.9980 0.9973 0.9963 0.9951 0.9936 0.9918 0.9896 0.9870 0.9839 0.9803
6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994 0.9991 0.9988 0.9984 0.9979 0.9973 0.9965
7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996
8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
0 0.0492 0.0430 0.0374 0.0326 0.0282 0.0245 0.0211 0.0182 0.0157 0.0135 0.0115 0.0098 0.0084 0.0071 0.0060 0.0051 0.0043 0.0036 0.0030 0.0025 0.0021 0.0017 0.0014 0.0012 0.0010
n = 10
1 0.2222 0.2019 0.1830 0.1655 0.1493 0.1344 0.1206 0.1080 0.0965 0.0860 0.0764 0.0677 0.0598 0.0527 0.0464 0.0406 0.0355 0.0309 0.0269 0.0233 0.0201 0.0173 0.0148 0.0126 0.0107
2 0.4958 0.4665 0.4378 0.4099 0.3828 0.3566 0.3313 0.3070 0.2838 0.2616 0.2405 0.2206 0.2017 0.1840 0.1673 0.1517 0.1372 0.1236 0.1111 0.0996 0.0889 0.0791 0.0702 0.0621 0.0547
3 0.7521 0.7274 0.7021 0.6761 0.6496 0.6228 0.5956 0.5684 0.5411 0.5138 0.4868 0.4600 0.4336 0.4077 0.3823 0.3575 0.3335 0.3102 0.2877 0.2660 0.2453 0.2255 0.2067 0.1888 0.1719
4 0.9096 0.8963 0.8819 0.8663 0.8497 0.8321 0.8133 0.7936 0.7730 0.7515 0.7292 0.7061 0.6823 0.6580 0.6331 0.6078 0.5822 0.5564 0.5304 0.5044 0.4784 0.4526 0.4270 0.4018 0.3770
5 0.9761 0.9713 0.9658 0.9596 0.9527 0.9449 0.9363 0.9268 0.9164 0.9051 0.8928 0.8795 0.8652 0.8500 0.8338 0.8166 0.7984 0.7793 0.7593 0.7384 0.7168 0.6943 0.6712 0.6474 0.6230
6 0.9955 0.9944 0.9930 0.9913 0.9894 0.9871 0.9845 0.9815 0.9780 0.9740 0.9695 0.9644 0.9587 0.9523 0.9452 0.9374 0.9288 0.9194 0.9092 0.8980 0.8859 0.8729 0.8590 0.8440 0.8281
7 0.9994 0.9993 0.9990 0.9988 0.9984 0.9980 0.9975 0.9968 0.9961 0.9952 0.9941 0.9929 0.9914 0.9897 0.9877 0.9854 0.9828 0.9798 0.9764 0.9726 0.9683 0.9634 0.9580 0.9520 0.9453
8 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9997 0.9997 0.9996 0.9995 0.9993 0.9991 0.9989 0.9986 0.9983 0.9979 0.9975 0.9969 0.9963 0.9955 0.9946 0.9935 0.9923 0.9909 0.9893
9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9997 0.9996 0.9995 0.9994 0.9992 0.9990
10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
X ∼ B(n, p) P (X ≤ x)
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.8953 0.8007 0.7153 0.6382 0.5688 0.5063 0.4501 0.3996 0.3544 0.3138 0.2775 0.2451 0.2161 0.1903 0.1673 0.1469 0.1288 0.1127 0.0985 0.0859 0.0748 0.0650 0.0564 0.0489 0.0422
1 0.9948 0.9805 0.9587 0.9308 0.8981 0.8618 0.8228 0.7819 0.7399 0.6974 0.6548 0.6127 0.5714 0.5311 0.4922 0.4547 0.4189 0.3849 0.3526 0.3221 0.2935 0.2667 0.2418 0.2186 0.1971
2 0.9998 0.9988 0.9963 0.9917 0.9848 0.9752 0.9630 0.9481 0.9305 0.9104 0.8880 0.8634 0.8368 0.8085 0.7788 0.7479 0.7161 0.6836 0.6506 0.6174 0.5842 0.5512 0.5186 0.4866 0.4552
3 1.0000 1.0000 0.9998 0.9993 0.9984 0.9970 0.9947 0.9915 0.9871 0.9815 0.9744 0.9659 0.9558 0.9440 0.9306 0.9154 0.8987 0.8803 0.8603 0.8389 0.8160 0.7919 0.7667 0.7404 0.7133
4 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9995 0.9990 0.9983 0.9972 0.9958 0.9939 0.9913 0.9881 0.9841 0.9793 0.9734 0.9666 0.9587 0.9496 0.9393 0.9277 0.9149 0.9008 0.8854
5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9995 0.9992 0.9988 0.9982 0.9973 0.9963 0.9949 0.9932 0.9910 0.9883 0.9852 0.9814 0.9769 0.9717 0.9657
6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9995 0.9993 0.9990 0.9986 0.9980 0.9973 0.9965 0.9954 0.9941 0.9924
7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9998 0.9997 0.9995 0.9993 0.9991 0.9988
8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999
9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
11 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
0 0.0364 0.0314 0.0270 0.0231 0.0198 0.0169 0.0144 0.0122 0.0104 0.0088 0.0074 0.0062 0.0052 0.0044 0.0036 0.0030 0.0025 0.0021 0.0017 0.0014 0.0011 0.0009 0.0008 0.0006 0.0005
n = 11
1 0.1773 0.1590 0.1423 0.1270 0.1130 0.1003 0.0888 0.0784 0.0690 0.0606 0.0530 0.0463 0.0403 0.0350 0.0302 0.0261 0.0224 0.0192 0.0164 0.0139 0.0118 0.0100 0.0084 0.0070 0.0059
2 0.4247 0.3951 0.3665 0.3390 0.3127 0.2877 0.2639 0.2413 0.2201 0.2001 0.1814 0.1640 0.1478 0.1328 0.1189 0.1062 0.0945 0.0838 0.0740 0.0652 0.0572 0.0501 0.0436 0.0378 0.0327
3 0.6854 0.6570 0.6281 0.5989 0.5696 0.5402 0.5110 0.4821 0.4536 0.4256 0.3981 0.3714 0.3455 0.3204 0.2963 0.2731 0.2510 0.2300 0.2100 0.1911 0.1734 0.1567 0.1412 0.1267 0.1133
4 0.8687 0.8507 0.8315 0.8112 0.7897 0.7672 0.7437 0.7193 0.6941 0.6683 0.6419 0.6150 0.5878 0.5603 0.5328 0.5052 0.4777 0.4505 0.4236 0.3971 0.3712 0.3459 0.3213 0.2974 0.2744
5 0.9588 0.9510 0.9423 0.9326 0.9218 0.9099 0.8969 0.8829 0.8676 0.8513 0.8339 0.8153 0.7957 0.7751 0.7535 0.7310 0.7076 0.6834 0.6586 0.6331 0.6071 0.5807 0.5540 0.5271 0.5000
6 0.9905 0.9881 0.9854 0.9821 0.9784 0.9740 0.9691 0.9634 0.9570 0.9499 0.9419 0.9330 0.9232 0.9124 0.9006 0.8879 0.8740 0.8592 0.8432 0.8262 0.8081 0.7890 0.7688 0.7477 0.7256
7 0.9984 0.9979 0.9973 0.9966 0.9957 0.9946 0.9933 0.9918 0.9899 0.9878 0.9852 0.9823 0.9790 0.9751 0.9707 0.9657 0.9601 0.9539 0.9468 0.9390 0.9304 0.9209 0.9105 0.8991 0.8867
8 0.9998 0.9998 0.9997 0.9996 0.9994 0.9992 0.9990 0.9987 0.9984 0.9980 0.9974 0.9968 0.9961 0.9952 0.9941 0.9928 0.9913 0.9896 0.9875 0.9852 0.9825 0.9794 0.9759 0.9718 0.9673
9 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9995 0.9994 0.9993 0.9991 0.9988 0.9986 0.9982 0.9978 0.9973 0.9967 0.9960 0.9951 0.9941
10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9998 0.9997 0.9996 0.9995
11 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.8864 0.7847 0.6938 0.6127 0.5404 0.4759 0.4186 0.3677 0.3225 0.2824 0.2470 0.2157 0.1880 0.1637 0.1422 0.1234 0.1069 0.0924 0.0798 0.0687 0.0591 0.0507 0.0434 0.0371 0.0317
1 0.9938 0.9769 0.9514 0.9191 0.8816 0.8405 0.7967 0.7513 0.7052 0.6590 0.6133 0.5686 0.5252 0.4834 0.4435 0.4055 0.3696 0.3359 0.3043 0.2749 0.2476 0.2224 0.1991 0.1778 0.1584
2 0.9998 0.9985 0.9952 0.9893 0.9804 0.9684 0.9532 0.9348 0.9134 0.8891 0.8623 0.8333 0.8023 0.7697 0.7358 0.7010 0.6656 0.6298 0.5940 0.5583 0.5232 0.4886 0.4550 0.4222 0.3907
3 1.0000 0.9999 0.9997 0.9990 0.9978 0.9957 0.9925 0.9880 0.9820 0.9744 0.9649 0.9536 0.9403 0.9250 0.9078 0.8886 0.8676 0.8448 0.8205 0.7946 0.7674 0.7390 0.7096 0.6795 0.6488
4 1.0000 1.0000 1.0000 0.9999 0.9998 0.9996 0.9991 0.9984 0.9973 0.9957 0.9935 0.9905 0.9867 0.9819 0.9761 0.9690 0.9607 0.9511 0.9400 0.9274 0.9134 0.8979 0.8808 0.8623 0.8424
5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9995 0.9991 0.9986 0.9978 0.9967 0.9954 0.9935 0.9912 0.9884 0.9849 0.9806 0.9755 0.9696 0.9626 0.9547 0.9456
6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9996 0.9993 0.9990 0.9985 0.9979 0.9971 0.9961 0.9948 0.9932 0.9911 0.9887 0.9857
7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994 0.9992 0.9989 0.9984 0.9979 0.9972
8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996
9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
11 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
12 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
0 0.0270 0.0229 0.0194 0.0164 0.0138 0.0116 0.0098 0.0082 0.0068 0.0057 0.0047 0.0039 0.0032 0.0027 0.0022 0.0018 0.0014 0.0012 0.0010 0.0008 0.0006 0.0005 0.0004 0.0003 0.0002
n = 12
1 0.1406 0.1245 0.1100 0.0968 0.0850 0.0744 0.0650 0.0565 0.0491 0.0424 0.0366 0.0315 0.0270 0.0230 0.0196 0.0166 0.0140 0.0118 0.0099 0.0083 0.0069 0.0057 0.0047 0.0039 0.0032
2 0.3603 0.3313 0.3037 0.2775 0.2528 0.2296 0.2078 0.1876 0.1687 0.1513 0.1352 0.1205 0.1069 0.0946 0.0834 0.0733 0.0642 0.0560 0.0487 0.0421 0.0363 0.0312 0.0267 0.0227 0.0193
3 0.6176 0.5863 0.5548 0.5235 0.4925 0.4619 0.4319 0.4027 0.3742 0.3467 0.3201 0.2947 0.2704 0.2472 0.2253 0.2047 0.1853 0.1671 0.1502 0.1345 0.1199 0.1066 0.0943 0.0832 0.0730
4 0.8210 0.7984 0.7746 0.7496 0.7237 0.6968 0.6692 0.6410 0.6124 0.5833 0.5541 0.5249 0.4957 0.4668 0.4382 0.4101 0.3825 0.3557 0.3296 0.3044 0.2802 0.2570 0.2348 0.2138 0.1938
5 0.9354 0.9240 0.9113 0.8974 0.8822 0.8657 0.8479 0.8289 0.8087 0.7873 0.7648 0.7412 0.7167 0.6913 0.6652 0.6384 0.6111 0.5833 0.5552 0.5269 0.4986 0.4703 0.4423 0.4145 0.3872
6 0.9822 0.9781 0.9733 0.9678 0.9614 0.9542 0.9460 0.9368 0.9266 0.9154 0.9030 0.8894 0.8747 0.8589 0.8418 0.8235 0.8041 0.7836 0.7620 0.7393 0.7157 0.6911 0.6657 0.6396 0.6128
7 0.9964 0.9953 0.9940 0.9924 0.9905 0.9882 0.9856 0.9824 0.9787 0.9745 0.9696 0.9641 0.9578 0.9507 0.9427 0.9338 0.9240 0.9131 0.9012 0.8883 0.8742 0.8589 0.8425 0.8249 0.8062
8 0.9995 0.9993 0.9990 0.9987 0.9983 0.9978 0.9972 0.9964 0.9955 0.9944 0.9930 0.9915 0.9896 0.9873 0.9847 0.9817 0.9782 0.9742 0.9696 0.9644 0.9585 0.9519 0.9445 0.9362 0.9270
9 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9995 0.9993 0.9992 0.9989 0.9986 0.9982 0.9978 0.9972 0.9965 0.9957 0.9947 0.9935 0.9921 0.9905 0.9886 0.9863 0.9837 0.9807
10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9995 0.9993 0.9991 0.9989 0.9986 0.9983 0.9979 0.9974 0.9968
11 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998
12 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
X ∼ B(n, p) P (X ≤ x)
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.8775 0.7690 0.6730 0.5882 0.5133 0.4474 0.3893 0.3383 0.2935 0.2542 0.2198 0.1898 0.1636 0.1408 0.1209 0.1037 0.0887 0.0758 0.0646 0.0550 0.0467 0.0396 0.0334 0.0282 0.0238
1 0.9928 0.9730 0.9436 0.9068 0.8646 0.8186 0.7702 0.7206 0.6707 0.6213 0.5730 0.5262 0.4814 0.4386 0.3983 0.3604 0.3249 0.2920 0.2616 0.2336 0.2080 0.1846 0.1633 0.1441 0.1267
2 0.9997 0.9980 0.9938 0.9865 0.9755 0.9608 0.9422 0.9201 0.8946 0.8661 0.8349 0.8015 0.7663 0.7296 0.6920 0.6537 0.6152 0.5769 0.5389 0.5017 0.4653 0.4301 0.3961 0.3636 0.3326
3 1.0000 0.9999 0.9995 0.9986 0.9969 0.9940 0.9897 0.9837 0.9758 0.9658 0.9536 0.9391 0.9224 0.9033 0.8820 0.8586 0.8333 0.8061 0.7774 0.7473 0.7161 0.6839 0.6511 0.6178 0.5843
4 1.0000 1.0000 1.0000 0.9999 0.9997 0.9993 0.9987 0.9976 0.9959 0.9935 0.9903 0.9861 0.9807 0.9740 0.9658 0.9562 0.9449 0.9319 0.9173 0.9009 0.8827 0.8629 0.8415 0.8184 0.7940
5 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9997 0.9995 0.9991 0.9985 0.9976 0.9964 0.9947 0.9925 0.9896 0.9861 0.9817 0.9763 0.9700 0.9625 0.9538 0.9438 0.9325 0.9198
6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9995 0.9992 0.9987 0.9981 0.9973 0.9962 0.9948 0.9930 0.9907 0.9880 0.9846 0.9805 0.9757
7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994 0.9991 0.9988 0.9983 0.9976 0.9968 0.9957 0.9944
8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9998 0.9996 0.9995 0.9993 0.9990
9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999
10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
11 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
12 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
0 0.0200 0.0167 0.0140 0.0117 0.0097 0.0080 0.0066 0.0055 0.0045 0.0037 0.0030 0.0025 0.0020 0.0016 0.0013 0.0010 0.0008 0.0007 0.0005 0.0004 0.0003 0.0003 0.0002 0.0002 0.0001
n = 13
1 0.1111 0.0971 0.0846 0.0735 0.0637 0.0550 0.0473 0.0406 0.0347 0.0296 0.0251 0.0213 0.0179 0.0151 0.0126 0.0105 0.0088 0.0072 0.0060 0.0049 0.0040 0.0033 0.0026 0.0021 0.0017
2 0.3032 0.2755 0.2495 0.2251 0.2025 0.1815 0.1621 0.1443 0.1280 0.1132 0.0997 0.0875 0.0765 0.0667 0.0579 0.0501 0.0431 0.0370 0.0316 0.0269 0.0228 0.0192 0.0162 0.0135 0.0112
3 0.5507 0.5174 0.4845 0.4522 0.4206 0.3899 0.3602 0.3317 0.3043 0.2783 0.2536 0.2302 0.2083 0.1877 0.1686 0.1508 0.1344 0.1193 0.1055 0.0929 0.0815 0.0712 0.0619 0.0536 0.0461
4 0.7681 0.7411 0.7130 0.6840 0.6543 0.6240 0.5933 0.5624 0.5314 0.5005 0.4699 0.4397 0.4101 0.3812 0.3530 0.3258 0.2997 0.2746 0.2507 0.2279 0.2065 0.1863 0.1674 0.1498 0.1334
5 0.9056 0.8901 0.8730 0.8545 0.8346 0.8133 0.7907 0.7669 0.7419 0.7159 0.6889 0.6612 0.6327 0.6038 0.5744 0.5448 0.5151 0.4854 0.4559 0.4268 0.3981 0.3701 0.3427 0.3162 0.2905
6 0.9701 0.9635 0.9560 0.9473 0.9376 0.9267 0.9146 0.9012 0.8865 0.8705 0.8532 0.8346 0.8147 0.7935 0.7712 0.7476 0.7230 0.6975 0.6710 0.6437 0.6158 0.5873 0.5585 0.5293 0.5000
7 0.9927 0.9907 0.9882 0.9853 0.9818 0.9777 0.9729 0.9674 0.9610 0.9538 0.9456 0.9365 0.9262 0.9149 0.9023 0.8886 0.8736 0.8574 0.8400 0.8212 0.8012 0.7800 0.7576 0.7341 0.7095
8 0.9987 0.9982 0.9976 0.9969 0.9960 0.9948 0.9935 0.9918 0.9898 0.9874 0.9846 0.9813 0.9775 0.9730 0.9679 0.9621 0.9554 0.9480 0.9395 0.9302 0.9197 0.9082 0.8955 0.8817 0.8666
9 0.9998 0.9997 0.9996 0.9995 0.9993 0.9991 0.9988 0.9985 0.9980 0.9975 0.9968 0.9960 0.9949 0.9937 0.9922 0.9904 0.9883 0.9859 0.9830 0.9797 0.9758 0.9713 0.9662 0.9604 0.9539
10 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9997 0.9997 0.9995 0.9994 0.9992 0.9990 0.9987 0.9983 0.9979 0.9973 0.9967 0.9959 0.9949 0.9937 0.9923 0.9907 0.9888
11 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9995 0.9993 0.9991 0.9989 0.9986 0.9983
12 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999
13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
X ∼ B(n, p) P (X ≤ x)
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.8687 0.7536 0.6528 0.5647 0.4877 0.4205 0.3620 0.3112 0.2670 0.2288 0.1956 0.1670 0.1423 0.1211 0.1028 0.0871 0.0736 0.0621 0.0523 0.0440 0.0369 0.0309 0.0258 0.0214 0.0178
1 0.9916 0.9690 0.9355 0.8941 0.8470 0.7963 0.7436 0.6900 0.6368 0.5846 0.5342 0.4859 0.4401 0.3969 0.3567 0.3193 0.2848 0.2531 0.2242 0.1979 0.1741 0.1527 0.1335 0.1163 0.1010
2 0.9997 0.9975 0.9923 0.9833 0.9699 0.9522 0.9302 0.9042 0.8745 0.8416 0.8061 0.7685 0.7292 0.6889 0.6479 0.6068 0.5659 0.5256 0.4862 0.4481 0.4113 0.3761 0.3426 0.3109 0.2811
3 1.0000 0.9999 0.9994 0.9981 0.9958 0.9920 0.9864 0.9786 0.9685 0.9559 0.9406 0.9226 0.9021 0.8790 0.8535 0.8258 0.7962 0.7649 0.7321 0.6982 0.6634 0.6281 0.5924 0.5568 0.5213
4 1.0000 1.0000 1.0000 0.9998 0.9996 0.9990 0.9980 0.9965 0.9941 0.9908 0.9863 0.9804 0.9731 0.9641 0.9533 0.9406 0.9259 0.9093 0.8907 0.8702 0.8477 0.8235 0.7977 0.7703 0.7415
5 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9996 0.9992 0.9985 0.9976 0.9962 0.9943 0.9918 0.9885 0.9843 0.9791 0.9727 0.9651 0.9561 0.9457 0.9338 0.9203 0.9051 0.8883
6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9994 0.9991 0.9985 0.9978 0.9968 0.9954 0.9936 0.9913 0.9884 0.9848 0.9804 0.9752 0.9690 0.9617
7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9995 0.9992 0.9988 0.9983 0.9976 0.9967 0.9955 0.9940 0.9921 0.9897
8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994 0.9992 0.9989 0.9984 0.9978
9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9998 0.9997
10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
11 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
12 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
0 0.0148 0.0122 0.0101 0.0083 0.0068 0.0055 0.0045 0.0037 0.0030 0.0024 0.0019 0.0016 0.0012 0.0010 0.0008 0.0006 0.0005 0.0004 0.0003 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001
n = 14
1 0.0874 0.0754 0.0648 0.0556 0.0475 0.0404 0.0343 0.0290 0.0244 0.0205 0.0172 0.0143 0.0119 0.0098 0.0081 0.0066 0.0054 0.0044 0.0036 0.0029 0.0023 0.0019 0.0015 0.0012 0.0009
2 0.2533 0.2273 0.2033 0.1812 0.1608 0.1423 0.1254 0.1101 0.0963 0.0839 0.0729 0.0630 0.0543 0.0466 0.0398 0.0339 0.0287 0.0242 0.0203 0.0170 0.0142 0.0117 0.0097 0.0079 0.0065
3 0.4864 0.4521 0.4187 0.3863 0.3552 0.3253 0.2968 0.2699 0.2444 0.2205 0.1982 0.1774 0.1582 0.1405 0.1243 0.1095 0.0961 0.0839 0.0730 0.0632 0.0545 0.0468 0.0399 0.0339 0.0287
4 0.7116 0.6807 0.6491 0.6168 0.5842 0.5514 0.5187 0.4862 0.4542 0.4227 0.3920 0.3622 0.3334 0.3057 0.2793 0.2541 0.2303 0.2078 0.1868 0.1672 0.1490 0.1322 0.1167 0.1026 0.0898
5 0.8699 0.8498 0.8282 0.8051 0.7805 0.7546 0.7276 0.6994 0.6703 0.6405 0.6101 0.5792 0.5481 0.5169 0.4859 0.4550 0.4246 0.3948 0.3656 0.3373 0.3100 0.2837 0.2585 0.2346 0.2120
6 0.9533 0.9437 0.9327 0.9204 0.9067 0.8916 0.8750 0.8569 0.8374 0.8164 0.7941 0.7704 0.7455 0.7195 0.6925 0.6645 0.6357 0.6063 0.5764 0.5461 0.5157 0.4852 0.4549 0.4249 0.3953
7 0.9868 0.9833 0.9792 0.9743 0.9685 0.9619 0.9542 0.9455 0.9357 0.9247 0.9124 0.8988 0.8838 0.8675 0.8499 0.8308 0.8104 0.7887 0.7656 0.7414 0.7160 0.6895 0.6620 0.6337 0.6047
8 0.9971 0.9962 0.9950 0.9935 0.9917 0.9895 0.9869 0.9837 0.9800 0.9757 0.9706 0.9647 0.9580 0.9503 0.9417 0.9320 0.9211 0.9090 0.8957 0.8811 0.8652 0.8480 0.8293 0.8094 0.7880
9 0.9995 0.9993 0.9991 0.9988 0.9983 0.9978 0.9971 0.9963 0.9952 0.9940 0.9924 0.9905 0.9883 0.9856 0.9825 0.9788 0.9745 0.9696 0.9639 0.9574 0.9500 0.9417 0.9323 0.9218 0.9102
10 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9995 0.9994 0.9992 0.9989 0.9986 0.9981 0.9976 0.9969 0.9961 0.9951 0.9939 0.9924 0.9907 0.9886 0.9861 0.9832 0.9798 0.9759 0.9713
11 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9997 0.9997 0.9995 0.9994 0.9992 0.9990 0.9987 0.9983 0.9978 0.9973 0.9966 0.9958 0.9947 0.9935
12 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9997 0.9997 0.9996 0.9994 0.9993 0.9991
13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999
14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
X ∼ B(n, p) P (X ≤ x)
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.8601 0.7386 0.6333 0.5421 0.4633 0.3953 0.3367 0.2863 0.2430 0.2059 0.1741 0.1470 0.1238 0.1041 0.0874 0.0731 0.0611 0.0510 0.0424 0.0352 0.0291 0.0241 0.0198 0.0163 0.0134
1 0.9904 0.9647 0.9270 0.8809 0.8290 0.7738 0.7168 0.6597 0.6035 0.5490 0.4969 0.4476 0.4013 0.3583 0.3186 0.2821 0.2489 0.2187 0.1915 0.1671 0.1453 0.1259 0.1087 0.0935 0.0802
2 0.9996 0.9970 0.9906 0.9797 0.9638 0.9429 0.9171 0.8870 0.8531 0.8159 0.7762 0.7346 0.6916 0.6480 0.6042 0.5608 0.5181 0.4766 0.4365 0.3980 0.3615 0.3269 0.2945 0.2642 0.2361
3 1.0000 0.9998 0.9992 0.9976 0.9945 0.9896 0.9825 0.9727 0.9601 0.9444 0.9258 0.9041 0.8796 0.8524 0.8227 0.7908 0.7571 0.7218 0.6854 0.6482 0.6105 0.5726 0.5350 0.4978 0.4613
4 1.0000 1.0000 0.9999 0.9998 0.9994 0.9986 0.9972 0.9950 0.9918 0.9873 0.9813 0.9735 0.9639 0.9522 0.9383 0.9222 0.9039 0.8833 0.8606 0.8358 0.8090 0.7805 0.7505 0.7190 0.6865
5 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9997 0.9993 0.9987 0.9978 0.9963 0.9943 0.9916 0.9879 0.9832 0.9773 0.9700 0.9613 0.9510 0.9389 0.9252 0.9095 0.8921 0.8728 0.8516
6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9994 0.9990 0.9985 0.9976 0.9964 0.9948 0.9926 0.9898 0.9863 0.9819 0.9766 0.9702 0.9626 0.9537 0.9434
7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9996 0.9994 0.9990 0.9986 0.9979 0.9970 0.9958 0.9942 0.9922 0.9896 0.9865 0.9827
8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9995 0.9992 0.9989 0.9984 0.9977 0.9969 0.9958
9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994 0.9992
10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999
11 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
12 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
15 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
0 0.0109 0.0089 0.0072 0.0059 0.0047 0.0038 0.0031 0.0025 0.0020 0.0016 0.0012 0.0010 0.0008 0.0006 0.0005 0.0004 0.0003 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0000 0.0000
n = 15
1 0.0685 0.0583 0.0495 0.0419 0.0353 0.0296 0.0248 0.0206 0.0171 0.0142 0.0117 0.0096 0.0078 0.0064 0.0052 0.0042 0.0034 0.0027 0.0021 0.0017 0.0013 0.0010 0.0008 0.0006 0.0005
2 0.2101 0.1863 0.1645 0.1447 0.1268 0.1107 0.0962 0.0833 0.0719 0.0617 0.0528 0.0450 0.0382 0.0322 0.0271 0.0227 0.0189 0.0157 0.0130 0.0107 0.0087 0.0071 0.0057 0.0046 0.0037
3 0.4258 0.3914 0.3584 0.3268 0.2969 0.2686 0.2420 0.2171 0.1940 0.1727 0.1531 0.1351 0.1187 0.1039 0.0905 0.0785 0.0678 0.0583 0.0498 0.0424 0.0359 0.0303 0.0254 0.0212 0.0176
4 0.6531 0.6190 0.5846 0.5500 0.5155 0.4813 0.4477 0.4148 0.3829 0.3519 0.3222 0.2938 0.2668 0.2413 0.2173 0.1948 0.1739 0.1546 0.1367 0.1204 0.1055 0.0920 0.0799 0.0690 0.0592
5 0.8287 0.8042 0.7780 0.7505 0.7216 0.6916 0.6607 0.6291 0.5968 0.5643 0.5316 0.4989 0.4665 0.4346 0.4032 0.3726 0.3430 0.3144 0.2869 0.2608 0.2359 0.2125 0.1905 0.1699 0.1509
6 0.9316 0.9183 0.9035 0.8870 0.8689 0.8491 0.8278 0.8049 0.7806 0.7548 0.7278 0.6997 0.6705 0.6405 0.6098 0.5786 0.5470 0.5153 0.4836 0.4522 0.4211 0.3905 0.3606 0.3316 0.3036
7 0.9781 0.9726 0.9662 0.9587 0.9500 0.9401 0.9289 0.9163 0.9023 0.8868 0.8698 0.8513 0.8313 0.8098 0.7869 0.7626 0.7370 0.7102 0.6824 0.6535 0.6238 0.5935 0.5626 0.5314 0.5000
8 0.9944 0.9927 0.9906 0.9879 0.9848 0.9810 0.9764 0.9711 0.9649 0.9578 0.9496 0.9403 0.9298 0.9180 0.9050 0.8905 0.8746 0.8573 0.8385 0.8182 0.7966 0.7735 0.7490 0.7233 0.6964
9 0.9989 0.9985 0.9979 0.9972 0.9963 0.9952 0.9938 0.9921 0.9901 0.9876 0.9846 0.9810 0.9768 0.9719 0.9662 0.9596 0.9521 0.9435 0.9339 0.9231 0.9110 0.8976 0.8829 0.8667 0.8491
10 0.9998 0.9998 0.9997 0.9995 0.9993 0.9991 0.9988 0.9984 0.9978 0.9972 0.9963 0.9953 0.9941 0.9925 0.9907 0.9884 0.9857 0.9826 0.9789 0.9745 0.9695 0.9637 0.9570 0.9494 0.9408
11 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9995 0.9994 0.9991 0.9989 0.9985 0.9981 0.9975 0.9968 0.9960 0.9949 0.9937 0.9921 0.9903 0.9881 0.9855 0.9824
12 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9995 0.9993 0.9991 0.9989 0.9986 0.9982 0.9977 0.9971 0.9963
13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9995
14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
15 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
X ∼ B(n, p) P (X ≤ x)
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.8515 0.7238 0.6143 0.5204 0.4401 0.3716 0.3131 0.2634 0.2211 0.1853 0.1550 0.1293 0.1077 0.0895 0.0743 0.0614 0.0507 0.0418 0.0343 0.0281 0.0230 0.0188 0.0153 0.0124 0.0100
1 0.9891 0.9601 0.9182 0.8673 0.8108 0.7511 0.6902 0.6299 0.5711 0.5147 0.4614 0.4115 0.3653 0.3227 0.2839 0.2487 0.2170 0.1885 0.1632 0.1407 0.1209 0.1035 0.0883 0.0750 0.0635
2 0.9995 0.9963 0.9887 0.9758 0.9571 0.9327 0.9031 0.8689 0.8306 0.7892 0.7455 0.7001 0.6539 0.6074 0.5614 0.5162 0.4723 0.4302 0.3899 0.3518 0.3161 0.2827 0.2517 0.2232 0.1971
3 1.0000 0.9998 0.9989 0.9968 0.9930 0.9868 0.9779 0.9658 0.9504 0.9316 0.9093 0.8838 0.8552 0.8237 0.7899 0.7540 0.7164 0.6777 0.6381 0.5981 0.5582 0.5186 0.4797 0.4417 0.4050
4 1.0000 1.0000 0.9999 0.9997 0.9991 0.9981 0.9962 0.9932 0.9889 0.9830 0.9752 0.9652 0.9529 0.9382 0.9209 0.9012 0.8789 0.8542 0.8273 0.7982 0.7673 0.7348 0.7009 0.6659 0.6302
5 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9995 0.9990 0.9981 0.9967 0.9947 0.9918 0.9880 0.9829 0.9765 0.9685 0.9588 0.9473 0.9338 0.9183 0.9008 0.8812 0.8595 0.8359 0.8103
6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9997 0.9995 0.9991 0.9985 0.9976 0.9962 0.9944 0.9920 0.9888 0.9847 0.9796 0.9733 0.9658 0.9568 0.9464 0.9343 0.9204
7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9996 0.9993 0.9989 0.9984 0.9976 0.9964 0.9949 0.9930 0.9905 0.9873 0.9834 0.9786 0.9729
8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9996 0.9993 0.9990 0.9985 0.9979 0.9970 0.9959 0.9944 0.9925
9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9998 0.9996 0.9994 0.9992 0.9988 0.9984
10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9997
11 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
12 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
15 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
0 0.0081 0.0065 0.0052 0.0042 0.0033 0.0026 0.0021 0.0016 0.0013 0.0010 0.0008 0.0006 0.0005 0.0004 0.0003 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000
n = 16
1 0.0535 0.0450 0.0377 0.0314 0.0261 0.0216 0.0178 0.0146 0.0120 0.0098 0.0079 0.0064 0.0052 0.0041 0.0033 0.0026 0.0021 0.0016 0.0013 0.0010 0.0008 0.0006 0.0005 0.0003 0.0003
2 0.1733 0.1518 0.1323 0.1149 0.0994 0.0856 0.0734 0.0626 0.0533 0.0451 0.0380 0.0319 0.0266 0.0222 0.0183 0.0151 0.0124 0.0101 0.0082 0.0066 0.0053 0.0042 0.0034 0.0027 0.0021
3 0.3697 0.3360 0.3041 0.2740 0.2459 0.2196 0.1953 0.1730 0.1525 0.1339 0.1170 0.1018 0.0881 0.0759 0.0651 0.0556 0.0473 0.0400 0.0336 0.0281 0.0234 0.0194 0.0160 0.0131 0.0106
4 0.5940 0.5575 0.5212 0.4853 0.4499 0.4154 0.3819 0.3496 0.3187 0.2892 0.2613 0.2351 0.2105 0.1877 0.1666 0.1471 0.1293 0.1131 0.0985 0.0853 0.0735 0.0630 0.0537 0.0456 0.0384
5 0.7831 0.7542 0.7239 0.6923 0.6598 0.6264 0.5926 0.5584 0.5241 0.4900 0.4562 0.4230 0.3906 0.3592 0.3288 0.2997 0.2720 0.2457 0.2208 0.1976 0.1759 0.1559 0.1374 0.1205 0.1051
6 0.9049 0.8875 0.8683 0.8474 0.8247 0.8003 0.7743 0.7469 0.7181 0.6881 0.6572 0.6254 0.5930 0.5602 0.5272 0.4942 0.4613 0.4289 0.3971 0.3660 0.3359 0.3068 0.2790 0.2524 0.2272
7 0.9660 0.9580 0.9486 0.9379 0.9256 0.9119 0.8965 0.8795 0.8609 0.8406 0.8187 0.7952 0.7702 0.7438 0.7161 0.6872 0.6572 0.6264 0.5949 0.5629 0.5306 0.4981 0.4657 0.4335 0.4018
8 0.9902 0.9873 0.9837 0.9794 0.9743 0.9683 0.9612 0.9530 0.9436 0.9329 0.9209 0.9074 0.8924 0.8758 0.8577 0.8381 0.8168 0.7940 0.7698 0.7441 0.7171 0.6889 0.6595 0.6293 0.5982
9 0.9977 0.9969 0.9959 0.9945 0.9929 0.9908 0.9883 0.9852 0.9815 0.9771 0.9720 0.9659 0.9589 0.9509 0.9417 0.9313 0.9195 0.9064 0.8919 0.8759 0.8584 0.8393 0.8186 0.7964 0.7728
10 0.9996 0.9994 0.9992 0.9989 0.9984 0.9979 0.9972 0.9963 0.9952 0.9938 0.9921 0.9900 0.9875 0.9845 0.9809 0.9766 0.9716 0.9658 0.9591 0.9514 0.9426 0.9326 0.9214 0.9089 0.8949
11 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9995 0.9993 0.9990 0.9987 0.9983 0.9977 0.9970 0.9962 0.9951 0.9938 0.9922 0.9902 0.9879 0.9851 0.9817 0.9778 0.9732 0.9678 0.9616
12 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9995 0.9993 0.9991 0.9988 0.9984 0.9979 0.9973 0.9965 0.9956 0.9945 0.9931 0.9914 0.9894
13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9994 0.9993 0.9990 0.9987 0.9984 0.9979
14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9997
15 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
X ∼ B(n, p) P (X ≤ x)
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.8429 0.7093 0.5958 0.4996 0.4181 0.3493 0.2912 0.2423 0.2012 0.1668 0.1379 0.1138 0.0937 0.0770 0.0631 0.0516 0.0421 0.0343 0.0278 0.0225 0.0182 0.0146 0.0118 0.0094 0.0075
1 0.9877 0.9554 0.9091 0.8535 0.7922 0.7283 0.6638 0.6005 0.5396 0.4818 0.4277 0.3777 0.3318 0.2901 0.2525 0.2187 0.1887 0.1621 0.1387 0.1182 0.1004 0.0849 0.0715 0.0600 0.0501
2 0.9994 0.9956 0.9866 0.9714 0.9497 0.9218 0.8882 0.8497 0.8073 0.7618 0.7142 0.6655 0.6164 0.5676 0.5198 0.4734 0.4289 0.3867 0.3468 0.3096 0.2751 0.2433 0.2141 0.1877 0.1637
3 1.0000 0.9997 0.9986 0.9960 0.9912 0.9836 0.9727 0.9581 0.9397 0.9174 0.8913 0.8617 0.8290 0.7935 0.7556 0.7159 0.6749 0.6331 0.5909 0.5489 0.5073 0.4667 0.4272 0.3893 0.3530
4 1.0000 1.0000 0.9999 0.9996 0.9988 0.9974 0.9949 0.9911 0.9855 0.9779 0.9679 0.9554 0.9402 0.9222 0.9013 0.8776 0.8513 0.8225 0.7913 0.7582 0.7234 0.6872 0.6500 0.6121 0.5739
5 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9993 0.9985 0.9973 0.9953 0.9925 0.9886 0.9834 0.9766 0.9681 0.9577 0.9452 0.9305 0.9136 0.8943 0.8727 0.8490 0.8230 0.7951 0.7653
6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9996 0.9992 0.9986 0.9977 0.9963 0.9944 0.9917 0.9882 0.9837 0.9780 0.9709 0.9623 0.9521 0.9402 0.9264 0.9106 0.8929
7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9996 0.9993 0.9989 0.9983 0.9973 0.9961 0.9943 0.9920 0.9891 0.9853 0.9806 0.9749 0.9680 0.9598
8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9995 0.9992 0.9988 0.9982 0.9974 0.9963 0.9949 0.9930 0.9906 0.9876
9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9995 0.9993 0.9989 0.9984 0.9978 0.9969
10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994
11 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999
12 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
15 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
17 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
0 0.0060 0.0047 0.0038 0.0030 0.0023 0.0018 0.0014 0.0011 0.0009 0.0007 0.0005 0.0004 0.0003 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
n = 17
1 0.0417 0.0346 0.0286 0.0235 0.0193 0.0157 0.0128 0.0104 0.0083 0.0067 0.0054 0.0043 0.0034 0.0027 0.0021 0.0016 0.0013 0.0010 0.0008 0.0006 0.0004 0.0003 0.0002 0.0002 0.0001
2 0.1422 0.1229 0.1058 0.0907 0.0774 0.0657 0.0556 0.0468 0.0392 0.0327 0.0272 0.0225 0.0185 0.0151 0.0123 0.0100 0.0080 0.0065 0.0052 0.0041 0.0032 0.0025 0.0020 0.0015 0.0012
3 0.3186 0.2863 0.2560 0.2279 0.2019 0.1781 0.1563 0.1366 0.1188 0.1028 0.0885 0.0759 0.0648 0.0550 0.0464 0.0390 0.0326 0.0271 0.0224 0.0184 0.0151 0.0123 0.0099 0.0080 0.0064
4 0.5357 0.4977 0.4604 0.4240 0.3887 0.3547 0.3222 0.2913 0.2622 0.2348 0.2094 0.1858 0.1640 0.1441 0.1260 0.1096 0.0949 0.0817 0.0699 0.0596 0.0505 0.0425 0.0356 0.0296 0.0245
5 0.7339 0.7011 0.6671 0.6323 0.5968 0.5610 0.5251 0.4895 0.4542 0.4197 0.3861 0.3535 0.3222 0.2923 0.2639 0.2372 0.2121 0.1887 0.1670 0.1471 0.1288 0.1122 0.0972 0.0838 0.0717
6 0.8732 0.8515 0.8279 0.8024 0.7752 0.7464 0.7162 0.6847 0.6521 0.6188 0.5848 0.5505 0.5161 0.4818 0.4478 0.4144 0.3818 0.3501 0.3195 0.2902 0.2623 0.2359 0.2110 0.1878 0.1662
7 0.9501 0.9389 0.9261 0.9116 0.8954 0.8773 0.8574 0.8358 0.8123 0.7872 0.7605 0.7324 0.7029 0.6722 0.6405 0.6080 0.5750 0.5415 0.5079 0.4743 0.4410 0.4082 0.3761 0.3448 0.3145
8 0.9839 0.9794 0.9739 0.9674 0.9597 0.9508 0.9405 0.9288 0.9155 0.9006 0.8841 0.8659 0.8459 0.8243 0.8011 0.7762 0.7498 0.7220 0.6928 0.6626 0.6313 0.5992 0.5665 0.5333 0.5000
9 0.9958 0.9943 0.9925 0.9902 0.9873 0.9838 0.9796 0.9746 0.9686 0.9617 0.9536 0.9443 0.9336 0.9216 0.9081 0.8930 0.8764 0.8581 0.8382 0.8166 0.7934 0.7686 0.7423 0.7145 0.6855
10 0.9991 0.9987 0.9982 0.9976 0.9968 0.9957 0.9943 0.9926 0.9905 0.9880 0.9849 0.9811 0.9766 0.9714 0.9652 0.9580 0.9497 0.9403 0.9295 0.9174 0.9038 0.8888 0.8721 0.8538 0.8338
11 0.9998 0.9998 0.9997 0.9995 0.9993 0.9991 0.9987 0.9983 0.9977 0.9970 0.9960 0.9949 0.9934 0.9916 0.9894 0.9867 0.9835 0.9797 0.9752 0.9699 0.9637 0.9566 0.9483 0.9389 0.9283
12 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9994 0.9992 0.9989 0.9985 0.9981 0.9975 0.9967 0.9958 0.9946 0.9931 0.9914 0.9892 0.9866 0.9835 0.9798 0.9755
13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9995 0.9994 0.9992 0.9989 0.9986 0.9981 0.9976 0.9969 0.9960 0.9950 0.9936
14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9995 0.9993 0.9991 0.9988
15 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999
16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
17 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
X ∼ B(n, p) P (X ≤ x)
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.8345 0.6951 0.5780 0.4796 0.3972 0.3283 0.2708 0.2229 0.1831 0.1501 0.1227 0.1002 0.0815 0.0662 0.0536 0.0434 0.0349 0.0281 0.0225 0.0180 0.0144 0.0114 0.0091 0.0072 0.0056
1 0.9862 0.9505 0.8997 0.8393 0.7735 0.7055 0.6378 0.5719 0.5091 0.4503 0.3958 0.3460 0.3008 0.2602 0.2241 0.1920 0.1638 0.1391 0.1176 0.0991 0.0831 0.0694 0.0577 0.0478 0.0395
2 0.9993 0.9948 0.9843 0.9667 0.9419 0.9102 0.8725 0.8298 0.7832 0.7338 0.6827 0.6310 0.5794 0.5287 0.4797 0.4327 0.3881 0.3462 0.3073 0.2713 0.2384 0.2084 0.1813 0.1570 0.1353
3 1.0000 0.9996 0.9982 0.9950 0.9891 0.9799 0.9667 0.9494 0.9277 0.9018 0.8718 0.8382 0.8014 0.7618 0.7202 0.6771 0.6331 0.5888 0.5446 0.5010 0.4586 0.4175 0.3782 0.3409 0.3057
4 1.0000 1.0000 0.9998 0.9994 0.9985 0.9966 0.9933 0.9884 0.9814 0.9718 0.9595 0.9442 0.9257 0.9041 0.8794 0.8518 0.8213 0.7884 0.7533 0.7164 0.6780 0.6387 0.5988 0.5586 0.5187
5 1.0000 1.0000 1.0000 0.9999 0.9998 0.9995 0.9990 0.9979 0.9962 0.9936 0.9898 0.9846 0.9778 0.9690 0.9581 0.9449 0.9292 0.9111 0.8903 0.8671 0.8414 0.8134 0.7832 0.7512 0.7175
6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9994 0.9988 0.9979 0.9966 0.9946 0.9919 0.9882 0.9833 0.9771 0.9694 0.9600 0.9487 0.9355 0.9201 0.9026 0.8829 0.8610
7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9994 0.9989 0.9983 0.9973 0.9959 0.9940 0.9914 0.9880 0.9837 0.9783 0.9717 0.9637 0.9542 0.9431
8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9995 0.9992 0.9987 0.9980 0.9971 0.9957 0.9940 0.9917 0.9888 0.9852 0.9807
9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9996 0.9994 0.9991 0.9986 0.9980 0.9972 0.9961 0.9946
10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994 0.9991 0.9988
11 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9998
12 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
15 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
17 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
18 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
0 0.0044 0.0035 0.0027 0.0021 0.0016 0.0013 0.0010 0.0007 0.0006 0.0004 0.0003 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
n = 18
1 0.0324 0.0265 0.0216 0.0176 0.0142 0.0114 0.0092 0.0073 0.0058 0.0046 0.0036 0.0028 0.0022 0.0017 0.0013 0.0010 0.0008 0.0006 0.0004 0.0003 0.0002 0.0002 0.0001 0.0001 0.0001
2 0.1161 0.0991 0.0842 0.0712 0.0600 0.0502 0.0419 0.0348 0.0287 0.0236 0.0193 0.0157 0.0127 0.0103 0.0082 0.0066 0.0052 0.0041 0.0032 0.0025 0.0019 0.0015 0.0011 0.0009 0.0007
3 0.2728 0.2422 0.2140 0.1881 0.1646 0.1432 0.1241 0.1069 0.0917 0.0783 0.0665 0.0561 0.0472 0.0394 0.0328 0.0271 0.0223 0.0182 0.0148 0.0120 0.0096 0.0077 0.0061 0.0048 0.0038
4 0.4792 0.4406 0.4032 0.3671 0.3327 0.2999 0.2691 0.2402 0.2134 0.1886 0.1659 0.1451 0.1263 0.1093 0.0942 0.0807 0.0687 0.0582 0.0490 0.0411 0.0342 0.0283 0.0233 0.0190 0.0154
5 0.6824 0.6462 0.6093 0.5719 0.5344 0.4971 0.4602 0.4241 0.3889 0.3550 0.3224 0.2914 0.2621 0.2345 0.2088 0.1849 0.1628 0.1427 0.1243 0.1077 0.0928 0.0795 0.0676 0.0572 0.0481
6 0.8370 0.8109 0.7829 0.7531 0.7217 0.6889 0.6550 0.6203 0.5849 0.5491 0.5133 0.4776 0.4424 0.4079 0.3743 0.3418 0.3105 0.2807 0.2524 0.2258 0.2009 0.1778 0.1564 0.1368 0.1189
7 0.9301 0.9153 0.8986 0.8800 0.8593 0.8367 0.8122 0.7859 0.7579 0.7283 0.6973 0.6651 0.6319 0.5979 0.5634 0.5287 0.4938 0.4592 0.4250 0.3915 0.3588 0.3272 0.2968 0.2678 0.2403
8 0.9751 0.9684 0.9605 0.9512 0.9404 0.9280 0.9139 0.8981 0.8804 0.8609 0.8396 0.8165 0.7916 0.7650 0.7368 0.7072 0.6764 0.6444 0.6115 0.5778 0.5438 0.5094 0.4751 0.4409 0.4073
9 0.9927 0.9903 0.9873 0.9836 0.9790 0.9736 0.9671 0.9595 0.9506 0.9403 0.9286 0.9153 0.9003 0.8837 0.8653 0.8451 0.8232 0.7996 0.7742 0.7473 0.7188 0.6890 0.6579 0.6258 0.5927
10 0.9982 0.9975 0.9966 0.9954 0.9939 0.9920 0.9896 0.9867 0.9831 0.9788 0.9736 0.9675 0.9603 0.9520 0.9424 0.9314 0.9189 0.9049 0.8893 0.8720 0.8530 0.8323 0.8098 0.7856 0.7597
11 0.9997 0.9995 0.9993 0.9990 0.9986 0.9980 0.9973 0.9964 0.9953 0.9938 0.9920 0.9898 0.9870 0.9837 0.9797 0.9750 0.9693 0.9628 0.9551 0.9463 0.9362 0.9247 0.9117 0.8972 0.8811
12 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9995 0.9992 0.9989 0.9986 0.9981 0.9974 0.9966 0.9956 0.9942 0.9926 0.9906 0.9882 0.9853 0.9817 0.9775 0.9725 0.9666 0.9598 0.9519
13 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9995 0.9993 0.9990 0.9987 0.9983 0.9978 0.9971 0.9962 0.9951 0.9937 0.9921 0.9900 0.9875 0.9846
14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9994 0.9993 0.9990 0.9987 0.9983 0.9977 0.9971 0.9962
15 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9995 0.9993
16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999
17 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
18 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
X ∼ B(n, p) P (X ≤ x)
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.8262 0.6812 0.5606 0.4604 0.3774 0.3086 0.2519 0.2051 0.1666 0.1351 0.1092 0.0881 0.0709 0.0569 0.0456 0.0364 0.0290 0.0230 0.0182 0.0144 0.0113 0.0089 0.0070 0.0054 0.0042
1 0.9847 0.9454 0.8900 0.8249 0.7547 0.6829 0.6121 0.5440 0.4798 0.4203 0.3658 0.3165 0.2723 0.2331 0.1985 0.1682 0.1419 0.1191 0.0996 0.0829 0.0687 0.0566 0.0465 0.0381 0.0310
2 0.9991 0.9939 0.9817 0.9616 0.9335 0.8979 0.8561 0.8092 0.7585 0.7054 0.6512 0.5968 0.5432 0.4911 0.4413 0.3941 0.3500 0.3090 0.2713 0.2369 0.2058 0.1778 0.1529 0.1308 0.1113
3 1.0000 0.9995 0.9978 0.9939 0.9868 0.9757 0.9602 0.9398 0.9147 0.8850 0.8510 0.8133 0.7725 0.7292 0.6841 0.6380 0.5915 0.5451 0.4995 0.4551 0.4123 0.3715 0.3329 0.2968 0.2631
4 1.0000 1.0000 0.9998 0.9993 0.9980 0.9956 0.9915 0.9853 0.9765 0.9648 0.9498 0.9315 0.9096 0.8842 0.8556 0.8238 0.7893 0.7524 0.7136 0.6733 0.6319 0.5900 0.5480 0.5064 0.4654
5 1.0000 1.0000 1.0000 0.9999 0.9998 0.9994 0.9986 0.9971 0.9949 0.9914 0.9865 0.9798 0.9710 0.9599 0.9463 0.9300 0.9109 0.8890 0.8643 0.8369 0.8071 0.7749 0.7408 0.7050 0.6678
6 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9996 0.9991 0.9983 0.9970 0.9952 0.9924 0.9887 0.9837 0.9772 0.9690 0.9589 0.9468 0.9324 0.9157 0.8966 0.8752 0.8513 0.8251
7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9997 0.9995 0.9991 0.9984 0.9974 0.9959 0.9939 0.9911 0.9874 0.9827 0.9767 0.9693 0.9604 0.9497 0.9371 0.9225
8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9995 0.9992 0.9986 0.9979 0.9968 0.9953 0.9933 0.9907 0.9873 0.9831 0.9778 0.9713
9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9996 0.9993 0.9990 0.9984 0.9977 0.9966 0.9953 0.9934 0.9911
10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9995 0.9993 0.9989 0.9984 0.9977
11 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9995
12 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999
13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
15 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
17 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
18 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
19 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
0 0.0033 0.0025 0.0019 0.0015 0.0011 0.0009 0.0007 0.0005 0.0004 0.0003 0.0002 0.0002 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
n = 19
1 0.0251 0.0203 0.0163 0.0131 0.0104 0.0083 0.0065 0.0051 0.0040 0.0031 0.0024 0.0019 0.0014 0.0011 0.0008 0.0006 0.0005 0.0004 0.0003 0.0002 0.0001 0.0001 0.0001 0.0001 0.0000
2 0.0943 0.0795 0.0667 0.0557 0.0462 0.0382 0.0314 0.0257 0.0209 0.0170 0.0137 0.0110 0.0087 0.0069 0.0055 0.0043 0.0033 0.0026 0.0020 0.0015 0.0012 0.0009 0.0007 0.0005 0.0004
3 0.2320 0.2035 0.1776 0.1542 0.1332 0.1144 0.0978 0.0831 0.0703 0.0591 0.0495 0.0412 0.0341 0.0281 0.0230 0.0187 0.0151 0.0122 0.0097 0.0077 0.0061 0.0048 0.0037 0.0029 0.0022
4 0.4256 0.3871 0.3502 0.3152 0.2822 0.2514 0.2227 0.1963 0.1720 0.1500 0.1301 0.1122 0.0962 0.0821 0.0696 0.0587 0.0492 0.0410 0.0340 0.0280 0.0229 0.0186 0.0150 0.0121 0.0096
5 0.6295 0.5907 0.5516 0.5125 0.4739 0.4359 0.3990 0.3634 0.3293 0.2968 0.2661 0.2373 0.2105 0.1857 0.1629 0.1421 0.1233 0.1063 0.0912 0.0777 0.0658 0.0554 0.0463 0.0385 0.0318
6 0.7968 0.7664 0.7343 0.7005 0.6655 0.6295 0.5927 0.5555 0.5182 0.4812 0.4446 0.4087 0.3739 0.3403 0.3081 0.2774 0.2485 0.2213 0.1961 0.1727 0.1512 0.1316 0.1138 0.0978 0.0835
7 0.9059 0.8871 0.8662 0.8432 0.8180 0.7909 0.7619 0.7312 0.6990 0.6656 0.6310 0.5957 0.5599 0.5238 0.4878 0.4520 0.4168 0.3824 0.3491 0.3169 0.2862 0.2570 0.2294 0.2036 0.1796
8 0.9634 0.9541 0.9432 0.9306 0.9161 0.8997 0.8814 0.8611 0.8388 0.8145 0.7884 0.7605 0.7309 0.6998 0.6675 0.6340 0.5997 0.5647 0.5294 0.4940 0.4587 0.4238 0.3895 0.3561 0.3238
9 0.9881 0.9844 0.9798 0.9742 0.9674 0.9595 0.9501 0.9392 0.9267 0.9125 0.8965 0.8787 0.8590 0.8374 0.8139 0.7886 0.7615 0.7328 0.7026 0.6710 0.6383 0.6046 0.5701 0.5352 0.5000
10 0.9968 0.9956 0.9940 0.9920 0.9895 0.9863 0.9824 0.9777 0.9720 0.9653 0.9574 0.9482 0.9375 0.9253 0.9115 0.8960 0.8787 0.8596 0.8387 0.8159 0.7913 0.7649 0.7369 0.7072 0.6762
11 0.9993 0.9990 0.9985 0.9980 0.9972 0.9962 0.9949 0.9932 0.9911 0.9886 0.9854 0.9815 0.9769 0.9713 0.9648 0.9571 0.9482 0.9379 0.9262 0.9129 0.8979 0.8813 0.8628 0.8425 0.8204
12 0.9999 0.9998 0.9997 0.9996 0.9994 0.9991 0.9988 0.9983 0.9977 0.9969 0.9959 0.9946 0.9930 0.9909 0.9884 0.9854 0.9817 0.9773 0.9720 0.9658 0.9585 0.9500 0.9403 0.9291 0.9165
13 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9998 0.9997 0.9995 0.9993 0.9991 0.9987 0.9983 0.9977 0.9969 0.9960 0.9948 0.9933 0.9914 0.9891 0.9863 0.9829 0.9788 0.9739 0.9682
14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9995 0.9994 0.9991 0.9988 0.9984 0.9979 0.9972 0.9964 0.9954 0.9940 0.9924 0.9904
15 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9995 0.9993 0.9990 0.9987 0.9983 0.9978
16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996
17 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
18 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
19 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
X ∼ B(n, p) P (X ≤ x)
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
0 0.8179 0.6676 0.5438 0.4420 0.3585 0.2901 0.2342 0.1887 0.1516 0.1216 0.0972 0.0776 0.0617 0.0490 0.0388 0.0306 0.0241 0.0189 0.0148 0.0115 0.0090 0.0069 0.0054 0.0041 0.0032
1 0.9831 0.9401 0.8802 0.8103 0.7358 0.6605 0.5869 0.5169 0.4516 0.3917 0.3376 0.2891 0.2461 0.2084 0.1756 0.1471 0.1227 0.1018 0.0841 0.0692 0.0566 0.0461 0.0374 0.0302 0.0243
2 0.9990 0.9929 0.9790 0.9561 0.9245 0.8850 0.8390 0.7879 0.7334 0.6769 0.6198 0.5631 0.5080 0.4550 0.4049 0.3580 0.3146 0.2748 0.2386 0.2061 0.1770 0.1512 0.1284 0.1085 0.0913
3 1.0000 0.9994 0.9973 0.9926 0.9841 0.9710 0.9529 0.9294 0.9007 0.8670 0.8290 0.7873 0.7427 0.6959 0.6477 0.5990 0.5504 0.5026 0.4561 0.4114 0.3690 0.3289 0.2915 0.2569 0.2252
4 1.0000 1.0000 0.9997 0.9990 0.9974 0.9944 0.9893 0.9817 0.9710 0.9568 0.9390 0.9173 0.8917 0.8625 0.8298 0.7941 0.7557 0.7151 0.6729 0.6296 0.5858 0.5420 0.4986 0.4561 0.4148
5 1.0000 1.0000 1.0000 0.9999 0.9997 0.9991 0.9981 0.9962 0.9932 0.9887 0.9825 0.9740 0.9630 0.9493 0.9327 0.9130 0.8902 0.8644 0.8357 0.8042 0.7703 0.7343 0.6965 0.6573 0.6172
6 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9994 0.9987 0.9976 0.9959 0.9933 0.9897 0.9847 0.9781 0.9696 0.9591 0.9463 0.9311 0.9133 0.8929 0.8699 0.8443 0.8162 0.7858
7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9996 0.9992 0.9986 0.9976 0.9962 0.9941 0.9912 0.9873 0.9823 0.9759 0.9679 0.9581 0.9464 0.9325 0.9165 0.8982
8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9995 0.9992 0.9987 0.9979 0.9967 0.9951 0.9929 0.9900 0.9862 0.9814 0.9754 0.9680 0.9591
9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9996 0.9993 0.9989 0.9983 0.9974 0.9962 0.9946 0.9925 0.9897 0.9861
10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9996 0.9994 0.9991 0.9987 0.9981 0.9972 0.9961
11 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994 0.9991
12 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998
13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
15 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
17 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
18 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
19 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
20 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
0 0.0024 0.0018 0.0014 0.0011 0.0008 0.0006 0.0004 0.0003 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
n = 20
1 0.0195 0.0155 0.0123 0.0097 0.0076 0.0060 0.0047 0.0036 0.0028 0.0021 0.0016 0.0012 0.0009 0.0007 0.0005 0.0004 0.0003 0.0002 0.0002 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000
2 0.0763 0.0635 0.0526 0.0433 0.0355 0.0289 0.0235 0.0189 0.0152 0.0121 0.0096 0.0076 0.0060 0.0047 0.0036 0.0028 0.0021 0.0016 0.0012 0.0009 0.0007 0.0005 0.0004 0.0003 0.0002
3 0.1962 0.1700 0.1466 0.1256 0.1071 0.0908 0.0765 0.0642 0.0535 0.0444 0.0366 0.0300 0.0245 0.0198 0.0160 0.0128 0.0102 0.0080 0.0063 0.0049 0.0038 0.0029 0.0023 0.0017 0.0013
4 0.3752 0.3375 0.3019 0.2685 0.2375 0.2089 0.1827 0.1589 0.1374 0.1182 0.1011 0.0859 0.0726 0.0610 0.0510 0.0423 0.0349 0.0286 0.0233 0.0189 0.0152 0.0121 0.0096 0.0076 0.0059
5 0.5765 0.5357 0.4952 0.4553 0.4164 0.3787 0.3426 0.3083 0.2758 0.2454 0.2171 0.1910 0.1671 0.1453 0.1256 0.1079 0.0922 0.0783 0.0660 0.0553 0.0461 0.0381 0.0313 0.0255 0.0207
6 0.7533 0.7190 0.6831 0.6460 0.6080 0.5695 0.5307 0.4921 0.4540 0.4166 0.3803 0.3453 0.3118 0.2800 0.2500 0.2220 0.1959 0.1719 0.1499 0.1299 0.1119 0.0958 0.0814 0.0688 0.0577
7 0.8775 0.8545 0.8293 0.8018 0.7723 0.7409 0.7078 0.6732 0.6376 0.6010 0.5639 0.5265 0.4892 0.4522 0.4159 0.3804 0.3461 0.3132 0.2817 0.2520 0.2241 0.1980 0.1739 0.1518 0.1316
8 0.9485 0.9360 0.9216 0.9052 0.8867 0.8660 0.8432 0.8182 0.7913 0.7624 0.7317 0.6995 0.6659 0.6312 0.5956 0.5594 0.5229 0.4864 0.4501 0.4143 0.3793 0.3454 0.3127 0.2814 0.2517
9 0.9817 0.9762 0.9695 0.9615 0.9520 0.9409 0.9281 0.9134 0.8968 0.8782 0.8576 0.8350 0.8103 0.7837 0.7553 0.7252 0.6936 0.6606 0.6264 0.5914 0.5557 0.5196 0.4834 0.4475 0.4119
10 0.9945 0.9926 0.9900 0.9868 0.9829 0.9780 0.9721 0.9650 0.9566 0.9468 0.9355 0.9225 0.9077 0.8910 0.8725 0.8520 0.8295 0.8051 0.7788 0.7507 0.7209 0.6896 0.6568 0.6229 0.5881
11 0.9986 0.9981 0.9973 0.9962 0.9949 0.9931 0.9909 0.9881 0.9846 0.9804 0.9753 0.9692 0.9619 0.9534 0.9435 0.9321 0.9190 0.9042 0.8877 0.8692 0.8489 0.8266 0.8023 0.7762 0.7483
12 0.9997 0.9996 0.9994 0.9991 0.9987 0.9982 0.9975 0.9966 0.9955 0.9940 0.9921 0.9898 0.9868 0.9833 0.9790 0.9738 0.9676 0.9603 0.9518 0.9420 0.9306 0.9177 0.9031 0.8867 0.8684
13 1.0000 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994 0.9992 0.9989 0.9985 0.9979 0.9972 0.9963 0.9951 0.9935 0.9916 0.9893 0.9864 0.9828 0.9786 0.9735 0.9674 0.9603 0.9520 0.9423
14 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994 0.9991 0.9988 0.9984 0.9978 0.9971 0.9962 0.9950 0.9936 0.9917 0.9895 0.9867 0.9834 0.9793
15 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9994 0.9992 0.9989 0.9985 0.9980 0.9973 0.9965 0.9954 0.9941
16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9995 0.9993 0.9990 0.9987
17 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998
18 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
19 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
20 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
X ∼ P (λ) P (X ≤ x)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5
0 0.9048 0.8187 0.7408 0.6703 0.6065 0.5488 0.4966 0.4493 0.4066 0.3679 0.3329 0.3012 0.2725 0.2466 0.2231 0.2019 0.1827 0.1653 0.1496 0.1353 0.1225 0.1108 0.1003 0.0907 0.0821
1 0.9953 0.9825 0.9631 0.9384 0.9098 0.8781 0.8442 0.8088 0.7725 0.7358 0.6990 0.6626 0.6268 0.5918 0.5578 0.5249 0.4932 0.4628 0.4337 0.4060 0.3796 0.3546 0.3309 0.3084 0.2873
2 0.9998 0.9989 0.9964 0.9921 0.9856 0.9769 0.9659 0.9526 0.9371 0.9197 0.9004 0.8795 0.8571 0.8335 0.8088 0.7834 0.7572 0.7306 0.7037 0.6767 0.6496 0.6227 0.5960 0.5697 0.5438
3 1.0000 0.9999 0.9997 0.9992 0.9982 0.9966 0.9942 0.9909 0.9865 0.9810 0.9743 0.9662 0.9569 0.9463 0.9344 0.9212 0.9068 0.8913 0.8747 0.8571 0.8386 0.8194 0.7993 0.7787 0.7576
4 1.0000 1.0000 0.9999 0.9998 0.9996 0.9992 0.9986 0.9977 0.9963 0.9946 0.9923 0.9893 0.9857 0.9814 0.9763 0.9704 0.9636 0.9559 0.9473 0.9379 0.9275 0.9162 0.9041 0.8912
5 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9994 0.9990 0.9985 0.9978 0.9968 0.9955 0.9940 0.9920 0.9896 0.9868 0.9834 0.9796 0.9751 0.9700 0.9643 0.9580
6 1.0000 1.0000 1.0000 0.9999 0.9999 0.9997 0.9996 0.9994 0.9991 0.9987 0.9981 0.9974 0.9966 0.9955 0.9941 0.9925 0.9906 0.9884 0.9858
7 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994 0.9992 0.9989 0.9985 0.9980 0.9974 0.9967 0.9958
8 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9998 0.9997 0.9995 0.9994 0.9991 0.9989
9 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9997
10 1.0000 1.0000 1.0000 1.0000 0.9999
11 1.0000
2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0
0 0.0743 0.0672 0.0608 0.0550 0.0498 0.0450 0.0408 0.0369 0.0334 0.0302 0.0273 0.0247 0.0224 0.0202 0.0183 0.0166 0.0150 0.0136 0.0123 0.0111 0.0101 0.0091 0.0082 0.0074 0.0067
1 0.2674 0.2487 0.2311 0.2146 0.1991 0.1847 0.1712 0.1586 0.1468 0.1359 0.1257 0.1162 0.1074 0.0992 0.0916 0.0845 0.0780 0.0719 0.0663 0.0611 0.0563 0.0518 0.0477 0.0439 0.0404
2 0.5184 0.4936 0.4695 0.4460 0.4232 0.4012 0.3799 0.3594 0.3397 0.3208 0.3027 0.2854 0.2689 0.2531 0.2381 0.2238 0.2102 0.1974 0.1851 0.1736 0.1626 0.1523 0.1425 0.1333 0.1247
3 0.7360 0.7141 0.6919 0.6696 0.6472 0.6248 0.6025 0.5803 0.5584 0.5366 0.5152 0.4942 0.4735 0.4532 0.4335 0.4142 0.3954 0.3772 0.3594 0.3423 0.3257 0.3097 0.2942 0.2793 0.2650
4 0.8774 0.8629 0.8477 0.8318 0.8153 0.7982 0.7806 0.7626 0.7442 0.7254 0.7064 0.6872 0.6678 0.6484 0.6288 0.6093 0.5898 0.5704 0.5512 0.5321 0.5132 0.4946 0.4763 0.4582 0.4405
5 0.9510 0.9433 0.9349 0.9258 0.9161 0.9057 0.8946 0.8829 0.8705 0.8576 0.8441 0.8301 0.8156 0.8006 0.7851 0.7693 0.7531 0.7367 0.7199 0.7029 0.6858 0.6684 0.6510 0.6335 0.6160
6 0.9828 0.9794 0.9756 0.9713 0.9665 0.9612 0.9554 0.9490 0.9421 0.9347 0.9267 0.9182 0.9091 0.8995 0.8893 0.8786 0.8675 0.8558 0.8436 0.8311 0.8180 0.8046 0.7908 0.7767 0.7622
7 0.9947 0.9934 0.9919 0.9901 0.9881 0.9858 0.9832 0.9802 0.9769 0.9733 0.9692 0.9648 0.9599 0.9546 0.9489 0.9427 0.9361 0.9290 0.9214 0.9134 0.9049 0.8960 0.8867 0.8769 0.8666
8 0.9985 0.9981 0.9976 0.9969 0.9962 0.9953 0.9943 0.9931 0.9917 0.9901 0.9883 0.9863 0.9840 0.9815 0.9786 0.9755 0.9721 0.9683 0.9642 0.9597 0.9549 0.9497 0.9442 0.9382 0.9319
9 0.9996 0.9995 0.9993 0.9991 0.9989 0.9986 0.9982 0.9978 0.9973 0.9967 0.9960 0.9952 0.9942 0.9931 0.9919 0.9905 0.9889 0.9871 0.9851 0.9829 0.9805 0.9778 0.9749 0.9717 0.9682
10 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9995 0.9994 0.9992 0.9990 0.9987 0.9984 0.9981 0.9977 0.9972 0.9966 0.9959 0.9952 0.9943 0.9933 0.9922 0.9910 0.9896 0.9880 0.9863
11 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9995 0.9994 0.9993 0.9991 0.9989 0.9986 0.9983 0.9980 0.9976 0.9971 0.9966 0.9960 0.9953 0.9945
12 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9997 0.9996 0.9995 0.9993 0.9992 0.9990 0.9988 0.9986 0.9983 0.9980
13 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9997 0.9996 0.9995 0.9994 0.9993
14 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998
15 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999
16 1.0000 1.0000
5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5
0 0.0061 0.0055 0.0050 0.0045 0.0041 0.0037 0.0033 0.0030 0.0027 0.0025 0.0022 0.0020 0.0018 0.0017 0.0015 0.0014 0.0012 0.0011 0.0010 0.0009 0.0008 0.0007 0.0007 0.0006 0.0006
1 0.0372 0.0342 0.0314 0.0289 0.0266 0.0244 0.0224 0.0206 0.0189 0.0174 0.0159 0.0146 0.0134 0.0123 0.0113 0.0103 0.0095 0.0087 0.0080 0.0073 0.0067 0.0061 0.0056 0.0051 0.0047
2 0.1165 0.1088 0.1016 0.0948 0.0884 0.0824 0.0768 0.0715 0.0666 0.0620 0.0577 0.0536 0.0498 0.0463 0.0430 0.0400 0.0371 0.0344 0.0320 0.0296 0.0275 0.0255 0.0236 0.0219 0.0203
3 0.2513 0.2381 0.2254 0.2133 0.2017 0.1906 0.1800 0.1700 0.1604 0.1512 0.1425 0.1342 0.1264 0.1189 0.1118 0.1052 0.0988 0.0928 0.0871 0.0818 0.0767 0.0719 0.0674 0.0632 0.0591
4 0.4231 0.4061 0.3895 0.3733 0.3575 0.3422 0.3272 0.3127 0.2987 0.2851 0.2719 0.2592 0.2469 0.2351 0.2237 0.2127 0.2022 0.1920 0.1823 0.1730 0.1641 0.1555 0.1473 0.1395 0.1321
5 0.5984 0.5809 0.5635 0.5461 0.5289 0.5119 0.4950 0.4783 0.4619 0.4457 0.4298 0.4141 0.3988 0.3837 0.3690 0.3547 0.3406 0.3270 0.3137 0.3007 0.2881 0.2759 0.2640 0.2526 0.2414
6 0.7474 0.7324 0.7171 0.7017 0.6860 0.6703 0.6544 0.6384 0.6224 0.6063 0.5902 0.5742 0.5582 0.5423 0.5265 0.5108 0.4953 0.4799 0.4647 0.4497 0.4349 0.4204 0.4060 0.3920 0.3782
7 0.8560 0.8449 0.8335 0.8217 0.8095 0.7970 0.7841 0.7710 0.7576 0.7440 0.7301 0.7160 0.7017 0.6873 0.6728 0.6581 0.6433 0.6285 0.6136 0.5987 0.5838 0.5689 0.5541 0.5393 0.5246
8 0.9252 0.9181 0.9106 0.9027 0.8944 0.8857 0.8766 0.8672 0.8574 0.8472 0.8367 0.8259 0.8148 0.8033 0.7916 0.7796 0.7673 0.7548 0.7420 0.7291 0.7160 0.7027 0.6892 0.6757 0.6620
9 0.9644 0.9603 0.9559 0.9512 0.9462 0.9409 0.9352 0.9292 0.9228 0.9161 0.9090 0.9016 0.8939 0.8858 0.8774 0.8686 0.8596 0.8502 0.8405 0.8305 0.8202 0.8096 0.7988 0.7877 0.7764
10 0.9844 0.9823 0.9800 0.9775 0.9747 0.9718 0.9686 0.9651 0.9614 0.9574 0.9531 0.9486 0.9437 0.9386 0.9332 0.9274 0.9214 0.9151 0.9084 0.9015 0.8942 0.8867 0.8788 0.8707 0.8622
11 0.9937 0.9927 0.9916 0.9904 0.9890 0.9875 0.9859 0.9841 0.9821 0.9799 0.9776 0.9750 0.9723 0.9693 0.9661 0.9627 0.9591 0.9552 0.9510 0.9467 0.9420 0.9371 0.9319 0.9265 0.9208
12 0.9976 0.9972 0.9967 0.9962 0.9955 0.9949 0.9941 0.9932 0.9922 0.9912 0.9900 0.9887 0.9873 0.9857 0.9840 0.9821 0.9801 0.9779 0.9755 0.9730 0.9703 0.9673 0.9642 0.9609 0.9573
13 0.9992 0.9990 0.9988 0.9986 0.9983 0.9980 0.9977 0.9973 0.9969 0.9964 0.9958 0.9952 0.9945 0.9937 0.9929 0.9920 0.9909 0.9898 0.9885 0.9872 0.9857 0.9841 0.9824 0.9805 0.9784
14 0.9997 0.9997 0.9996 0.9995 0.9994 0.9993 0.9991 0.9990 0.9988 0.9986 0.9984 0.9981 0.9978 0.9974 0.9970 0.9966 0.9961 0.9956 0.9950 0.9943 0.9935 0.9927 0.9918 0.9908 0.9897
15 0.9999 0.9999 0.9999 0.9998 0.9998 0.9998 0.9997 0.9996 0.9996 0.9995 0.9994 0.9993 0.9992 0.9990 0.9988 0.9986 0.9984 0.9982 0.9979 0.9976 0.9972 0.9969 0.9964 0.9959 0.9954
16 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9997 0.9996 0.9996 0.9995 0.9994 0.9993 0.9992 0.9990 0.9989 0.9987 0.9985 0.9983 0.9980
17 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9998 0.9997 0.9997 0.9996 0.9996 0.9995 0.9994 0.9993 0.9992
18 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9998 0.9997 0.9997
19 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999
20 1.0000 1.0000 1.0000 1.0000 1.0000
X ∼ P (λ) P (X ≤ x)
7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9.0 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 10.0
0 0.0005 0.0005 0.0004 0.0004 0.0003 0.0003 0.0003 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0000
1 0.0043 0.0039 0.0036 0.0033 0.0030 0.0028 0.0025 0.0023 0.0021 0.0019 0.0018 0.0016 0.0015 0.0014 0.0012 0.0011 0.0010 0.0009 0.0009 0.0008 0.0007 0.0007 0.0006 0.0005 0.0005
2 0.0188 0.0174 0.0161 0.0149 0.0138 0.0127 0.0118 0.0109 0.0100 0.0093 0.0086 0.0079 0.0073 0.0068 0.0062 0.0058 0.0053 0.0049 0.0045 0.0042 0.0038 0.0035 0.0033 0.0030 0.0028
3 0.0554 0.0518 0.0485 0.0453 0.0424 0.0396 0.0370 0.0346 0.0323 0.0301 0.0281 0.0262 0.0244 0.0228 0.0212 0.0198 0.0184 0.0172 0.0160 0.0149 0.0138 0.0129 0.0120 0.0111 0.0103
4 0.1249 0.1181 0.1117 0.1055 0.0996 0.0940 0.0887 0.0837 0.0789 0.0744 0.0701 0.0660 0.0621 0.0584 0.0550 0.0517 0.0486 0.0456 0.0429 0.0403 0.0378 0.0355 0.0333 0.0312 0.0293
5 0.2307 0.2203 0.2103 0.2006 0.1912 0.1822 0.1736 0.1653 0.1573 0.1496 0.1422 0.1352 0.1284 0.1219 0.1157 0.1098 0.1041 0.0986 0.0935 0.0885 0.0838 0.0793 0.0750 0.0710 0.0671
6 0.3646 0.3514 0.3384 0.3257 0.3134 0.3013 0.2896 0.2781 0.2670 0.2562 0.2457 0.2355 0.2256 0.2160 0.2068 0.1978 0.1892 0.1808 0.1727 0.1649 0.1574 0.1502 0.1433 0.1366 0.1301
7 0.5100 0.4956 0.4812 0.4670 0.4530 0.4391 0.4254 0.4119 0.3987 0.3856 0.3728 0.3602 0.3478 0.3357 0.3239 0.3123 0.3010 0.2900 0.2792 0.2687 0.2584 0.2485 0.2388 0.2294 0.2202
8 0.6482 0.6343 0.6204 0.6065 0.5925 0.5786 0.5647 0.5507 0.5369 0.5231 0.5094 0.4958 0.4823 0.4689 0.4557 0.4426 0.4296 0.4168 0.4042 0.3918 0.3796 0.3676 0.3558 0.3442 0.3328
9 0.7649 0.7531 0.7411 0.7290 0.7166 0.7041 0.6915 0.6788 0.6659 0.6530 0.6400 0.6269 0.6137 0.6006 0.5874 0.5742 0.5611 0.5479 0.5349 0.5218 0.5089 0.4960 0.4832 0.4705 0.4579
10 0.8535 0.8445 0.8352 0.8257 0.8159 0.8058 0.7955 0.7850 0.7743 0.7634 0.7522 0.7409 0.7294 0.7178 0.7060 0.6941 0.6820 0.6699 0.6576 0.6453 0.6329 0.6205 0.6080 0.5955 0.5830
11 0.9148 0.9085 0.9020 0.8952 0.8881 0.8807 0.8731 0.8652 0.8571 0.8487 0.8400 0.8311 0.8220 0.8126 0.8030 0.7932 0.7832 0.7730 0.7626 0.7520 0.7412 0.7303 0.7193 0.7081 0.6968
12 0.9536 0.9496 0.9454 0.9409 0.9362 0.9313 0.9261 0.9207 0.9150 0.9091 0.9029 0.8965 0.8898 0.8829 0.8758 0.8684 0.8607 0.8529 0.8448 0.8364 0.8279 0.8191 0.8101 0.8009 0.7916
13 0.9762 0.9739 0.9714 0.9687 0.9658 0.9628 0.9595 0.9561 0.9524 0.9486 0.9445 0.9403 0.9358 0.9311 0.9261 0.9210 0.9156 0.9100 0.9042 0.8981 0.8919 0.8853 0.8786 0.8716 0.8645
14 0.9886 0.9873 0.9859 0.9844 0.9827 0.9810 0.9791 0.9771 0.9749 0.9726 0.9701 0.9675 0.9647 0.9617 0.9585 0.9552 0.9517 0.9480 0.9441 0.9400 0.9357 0.9312 0.9265 0.9216 0.9165
15 0.9948 0.9941 0.9934 0.9926 0.9918 0.9908 0.9898 0.9887 0.9875 0.9862 0.9848 0.9832 0.9816 0.9798 0.9780 0.9760 0.9738 0.9715 0.9691 0.9665 0.9638 0.9609 0.9579 0.9546 0.9513
16 0.9978 0.9974 0.9971 0.9967 0.9963 0.9958 0.9953 0.9947 0.9941 0.9934 0.9926 0.9918 0.9909 0.9899 0.9889 0.9878 0.9865 0.9852 0.9838 0.9823 0.9806 0.9789 0.9770 0.9751 0.9730
17 0.9991 0.9989 0.9988 0.9986 0.9984 0.9982 0.9979 0.9977 0.9973 0.9970 0.9966 0.9962 0.9957 0.9952 0.9947 0.9941 0.9934 0.9927 0.9919 0.9911 0.9902 0.9892 0.9881 0.9870 0.9857
18 0.9996 0.9996 0.9995 0.9994 0.9993 0.9992 0.9991 0.9990 0.9989 0.9987 0.9985 0.9983 0.9981 0.9978 0.9976 0.9973 0.9969 0.9966 0.9962 0.9957 0.9952 0.9947 0.9941 0.9935 0.9928
19 0.9999 0.9998 0.9998 0.9998 0.9997 0.9997 0.9997 0.9996 0.9995 0.9995 0.9994 0.9993 0.9992 0.9991 0.9989 0.9988 0.9986 0.9985 0.9983 0.9980 0.9978 0.9975 0.9972 0.9969 0.9965
20 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9998 0.9998 0.9997 0.9997 0.9996 0.9996 0.9995 0.9994 0.9993 0.9992 0.9991 0.9990 0.9989 0.9987 0.9986 0.9984
21 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9998 0.9998 0.9997 0.9997 0.9996 0.9996 0.9995 0.9995 0.9994 0.9993
22 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9998 0.9997 0.9997
23 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
24 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
X ∼ P (λ) P (X ≤ x)
11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0 24.0 25.0 26.0 27.0 28.0 29.0 30.0 31.0 32.0 33.0 34.0 35.0
0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
2 0.0012 0.0005 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
3 0.0049 0.0023 0.0011 0.0005 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
4 0.0151 0.0076 0.0037 0.0018 0.0009 0.0004 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
5 0.0375 0.0203 0.0107 0.0055 0.0028 0.0014 0.0007 0.0003 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
6 0.0786 0.0458 0.0259 0.0142 0.0076 0.0040 0.0021 0.0010 0.0005 0.0003 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
7 0.1432 0.0895 0.0540 0.0316 0.0180 0.0100 0.0054 0.0029 0.0015 0.0008 0.0004 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
8 0.2320 0.1550 0.0998 0.0621 0.0374 0.0220 0.0126 0.0071 0.0039 0.0021 0.0011 0.0006 0.0003 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
9 0.3405 0.2424 0.1658 0.1094 0.0699 0.0433 0.0261 0.0154 0.0089 0.0050 0.0028 0.0015 0.0008 0.0004 0.0002 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
10 0.4599 0.3472 0.2517 0.1757 0.1185 0.0774 0.0491 0.0304 0.0183 0.0108 0.0063 0.0035 0.0020 0.0011 0.0006 0.0003 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
11 0.5793 0.4616 0.3532 0.2600 0.1848 0.1270 0.0847 0.0549 0.0347 0.0214 0.0129 0.0076 0.0044 0.0025 0.0014 0.0008 0.0004 0.0002 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000
12 0.6887 0.5760 0.4631 0.3585 0.2676 0.1931 0.1350 0.0917 0.0606 0.0390 0.0245 0.0151 0.0091 0.0054 0.0031 0.0018 0.0010 0.0006 0.0003 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000
13 0.7813 0.6815 0.5730 0.4644 0.3632 0.2745 0.2009 0.1426 0.0984 0.0661 0.0434 0.0278 0.0174 0.0107 0.0065 0.0038 0.0022 0.0013 0.0007 0.0004 0.0002 0.0001 0.0001 0.0000 0.0000
14 0.8540 0.7720 0.6751 0.5704 0.4657 0.3675 0.2808 0.2081 0.1497 0.1049 0.0716 0.0477 0.0311 0.0198 0.0124 0.0076 0.0046 0.0027 0.0016 0.0009 0.0005 0.0003 0.0002 0.0001 0.0000
15 0.9074 0.8444 0.7636 0.6694 0.5681 0.4667 0.3715 0.2867 0.2148 0.1565 0.1111 0.0769 0.0520 0.0344 0.0223 0.0142 0.0088 0.0054 0.0033 0.0019 0.0011 0.0007 0.0004 0.0002 0.0001
16 0.9441 0.8987 0.8355 0.7559 0.6641 0.5660 0.4677 0.3751 0.2920 0.2211 0.1629 0.1170 0.0821 0.0563 0.0377 0.0248 0.0160 0.0101 0.0063 0.0039 0.0023 0.0014 0.0008 0.0005 0.0003
17 0.9678 0.9370 0.8905 0.8272 0.7489 0.6593 0.5640 0.4686 0.3784 0.2970 0.2270 0.1690 0.1228 0.0871 0.0605 0.0411 0.0274 0.0179 0.0115 0.0073 0.0045 0.0028 0.0017 0.0010 0.0006
18 0.9823 0.9626 0.9302 0.8826 0.8195 0.7423 0.6550 0.5622 0.4695 0.3814 0.3017 0.2325 0.1748 0.1283 0.0920 0.0646 0.0445 0.0300 0.0199 0.0129 0.0083 0.0052 0.0032 0.0020 0.0012
19 0.9907 0.9787 0.9573 0.9235 0.8752 0.8122 0.7363 0.6509 0.5606 0.4703 0.3843 0.3060 0.2377 0.1803 0.1336 0.0968 0.0687 0.0478 0.0326 0.0219 0.0144 0.0093 0.0060 0.0037 0.0023
20 0.9953 0.9884 0.9750 0.9521 0.9170 0.8682 0.8055 0.7307 0.6472 0.5591 0.4710 0.3869 0.3101 0.2426 0.1855 0.1387 0.1015 0.0727 0.0511 0.0353 0.0239 0.0159 0.0105 0.0068 0.0043
21 0.9977 0.9939 0.9859 0.9712 0.9469 0.9108 0.8615 0.7991 0.7255 0.6437 0.5577 0.4716 0.3894 0.3139 0.2473 0.1905 0.1436 0.1060 0.0767 0.0544 0.0379 0.0260 0.0175 0.0116 0.0076
22 0.9990 0.9970 0.9924 0.9833 0.9673 0.9418 0.9047 0.8551 0.7931 0.7206 0.6405 0.5564 0.4723 0.3917 0.3175 0.2517 0.1952 0.1483 0.1104 0.0806 0.0577 0.0406 0.0281 0.0191 0.0128
23 0.9995 0.9985 0.9960 0.9907 0.9805 0.9633 0.9367 0.8989 0.8490 0.7875 0.7160 0.6374 0.5551 0.4728 0.3939 0.3209 0.2559 0.1998 0.1529 0.1146 0.0844 0.0610 0.0433 0.0302 0.0208
24 0.9998 0.9993 0.9980 0.9950 0.9888 0.9777 0.9594 0.9317 0.8933 0.8432 0.7822 0.7117 0.6346 0.5540 0.4734 0.3959 0.3242 0.2599 0.2042 0.1572 0.1188 0.0881 0.0642 0.0460 0.0324
25 0.9999 0.9997 0.9990 0.9974 0.9938 0.9869 0.9748 0.9554 0.9269 0.8878 0.8377 0.7771 0.7077 0.6319 0.5529 0.4739 0.3979 0.3272 0.2637 0.2084 0.1615 0.1228 0.0918 0.0674 0.0486
26 1.0000 0.9999 0.9995 0.9987 0.9967 0.9925 0.9848 0.9718 0.9514 0.9221 0.8826 0.8324 0.7723 0.7038 0.6294 0.5519 0.4744 0.3997 0.3301 0.2673 0.2124 0.1656 0.1268 0.0953 0.0705
27 0.9999 0.9998 0.9994 0.9983 0.9959 0.9912 0.9827 0.9687 0.9475 0.9175 0.8775 0.8274 0.7677 0.7002 0.6270 0.5509 0.4749 0.4014 0.3329 0.2708 0.2162 0.1695 0.1306 0.0988
28 1.0000 0.9999 0.9997 0.9991 0.9978 0.9950 0.9897 0.9805 0.9657 0.9436 0.9129 0.8726 0.8225 0.7634 0.6967 0.6247 0.5500 0.4753 0.4031 0.3355 0.2741 0.2199 0.1733 0.1343
29 1.0000 0.9999 0.9996 0.9989 0.9973 0.9941 0.9882 0.9782 0.9626 0.9398 0.9085 0.8679 0.8179 0.7593 0.6935 0.6226 0.5492 0.4757 0.4047 0.3380 0.2773 0.2235 0.1770
30 0.9999 0.9998 0.9994 0.9986 0.9967 0.9930 0.9865 0.9758 0.9595 0.9360 0.9042 0.8633 0.8134 0.7553 0.6903 0.6206 0.5484 0.4761 0.4061 0.3404 0.2804 0.2269
31 1.0000 0.9999 0.9997 0.9993 0.9982 0.9960 0.9919 0.9848 0.9735 0.9564 0.9322 0.8999 0.8589 0.8092 0.7515 0.6874 0.6186 0.5476 0.4765 0.4076 0.3427 0.2833
32 1.0000 0.9999 0.9996 0.9990 0.9978 0.9953 0.9907 0.9831 0.9711 0.9533 0.9285 0.8958 0.8546 0.8051 0.7479 0.6845 0.6168 0.5468 0.4768 0.4089 0.3449
33 0.9999 0.9998 0.9995 0.9988 0.9973 0.9945 0.9895 0.9813 0.9686 0.9502 0.9249 0.8918 0.8505 0.8011 0.7444 0.6818 0.6150 0.5461 0.4772 0.4102
34 1.0000 0.9999 0.9998 0.9994 0.9985 0.9968 0.9936 0.9882 0.9794 0.9662 0.9472 0.9213 0.8879 0.8465 0.7973 0.7411 0.6792 0.6134 0.5454 0.4775
35 1.0000 0.9999 0.9997 0.9992 0.9982 0.9962 0.9927 0.9868 0.9775 0.9637 0.9441 0.9178 0.8841 0.8426 0.7936 0.7379 0.6767 0.6117 0.5448
36 0.9999 0.9998 0.9996 0.9990 0.9978 0.9956 0.9918 0.9854 0.9756 0.9612 0.9411 0.9144 0.8804 0.8389 0.7901 0.7349 0.6744 0.6102
37 1.0000 0.9999 0.9998 0.9995 0.9988 0.9974 0.9950 0.9908 0.9840 0.9737 0.9587 0.9381 0.9110 0.8768 0.8352 0.7867 0.7319 0.6721
38 1.0000 0.9999 0.9997 0.9993 0.9985 0.9970 0.9943 0.9897 0.9825 0.9717 0.9562 0.9352 0.9077 0.8732 0.8317 0.7834 0.7291
39 0.9999 0.9999 0.9996 0.9992 0.9983 0.9966 0.9936 0.9887 0.9810 0.9697 0.9537 0.9322 0.9044 0.8698 0.8283 0.7802
40 1.0000 0.9999 0.9998 0.9996 0.9990 0.9980 0.9961 0.9928 0.9875 0.9795 0.9677 0.9513 0.9293 0.9012 0.8664 0.8249
41 1.0000 0.9999 0.9998 0.9995 0.9988 0.9976 0.9955 0.9920 0.9864 0.9779 0.9657 0.9488 0.9265 0.8981 0.8631
42 1.0000 0.9999 0.9997 0.9993 0.9986 0.9973 0.9950 0.9911 0.9852 0.9763 0.9636 0.9464 0.9237 0.8950
43 0.9999 0.9998 0.9996 0.9992 0.9984 0.9969 0.9944 0.9903 0.9840 0.9747 0.9616 0.9439 0.9209
44 1.0000 0.9999 0.9998 0.9996 0.9991 0.9981 0.9965 0.9937 0.9894 0.9827 0.9730 0.9596 0.9415
45 1.0000 0.9999 0.9998 0.9995 0.9989 0.9978 0.9960 0.9931 0.9884 0.9814 0.9714 0.9575
46 0.9999 0.9999 0.9997 0.9994 0.9987 0.9975 0.9956 0.9924 0.9874 0.9801 0.9697
47 1.0000 0.9999 0.9998 0.9996 0.9992 0.9985 0.9972 0.9951 0.9917 0.9864 0.9788
48 1.0000 0.9999 0.9998 0.9996 0.9991 0.9983 0.9969 0.9946 0.9909 0.9854
49 1.0000 0.9999 0.9998 0.9995 0.9990 0.9981 0.9965 0.9940 0.9902
50 0.9999 0.9999 0.9997 0.9994 0.9988 0.9978 0.9961 0.9935
51 1.0000 0.9999 0.9998 0.9996 0.9993 0.9987 0.9976 0.9957
52 1.0000 0.9999 0.9998 0.9996 0.9992 0.9985 0.9973
53 0.9999 0.9999 0.9998 0.9995 0.9991 0.9983
54 1.0000 0.9999 0.9999 0.9997 0.9994 0.9989
55 1.0000 0.9999 0.9998 0.9997 0.9993
56 1.0000 0.9999 0.9998 0.9996
57 0.9999 0.9999 0.9998
58 1.0000 0.9999 0.9999
59 1.0000 0.9999
60 1.0000
Z ∼ N (0, 1) P (Z ≤ z)
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
−3.9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359
−3.8 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
−3.7 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
−3.6 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517
−3.5 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879
−3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
−3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549
−3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852
−3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133
−3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389
−2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621
−2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830
−2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015
−2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177
−2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319
−2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441
−2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545
−2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633
−2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706
−2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767
−1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817
−1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857
−1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890
−1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916
−1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936
−1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952
−1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964
−1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974
−1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981
−1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986
−0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990
−0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993
−0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995
−0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997
−0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998
−0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 3.5 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998
−0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 3.6 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
−0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 3.7 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
−0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 3.8 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
−0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 3.9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
P (Z < z) z P (Z < z) z P (Z < z) z P (Z < z) z P (Z < z) z P (Z < z) z P (Z < z) z

0.01 −2.3263 0.05 −1.6449 0.09 −1.3408 0.25 −0.6745 0.45 −0.1257 0.65 0.3853 0.85 1.0364
0.02 −2.0537 0.06 −1.5548 0.10 −1.2816 0.30 −0.5244 0.50 0.0000 0.70 0.5244 0.90 1.2816
0.03 −1.8808 0.07 −1.4758 0.15 −1.0364 0.35 −0.3853 0.55 0.1257 0.75 0.6745 0.95 1.6449
0.04 −1.7507 0.08 −1.4051 0.20 −0.8416 0.40 −0.2533 0.60 0.2533 0.80 0.8416 0.99 2.3263
Valores críticos para la distribución χ2 .
Valores de probabilidad anti-acumulada

gl 0.005 0.01 0.025 0.05 0.1 0.25 0.75 0.9 0.95 0.975 0.99 0.995
1 7.879 6.635 5.024 3.841 2.706 1.323 0.102 0.016 0.004 0.001 0.000 0.000
2 10.597 9.210 7.378 5.991 4.605 2.773 0.575 0.211 0.103 0.051 0.020 0.010
3 12.838 11.345 9.348 7.815 6.251 4.108 1.213 0.584 0.352 0.216 0.115 0.072
4 14.860 13.277 11.143 9.488 7.779 5.385 1.923 1.064 0.711 0.484 0.297 0.207
5 16.750 15.086 12.832 11.070 9.236 6.626 2.675 1.610 1.145 0.831 0.554 0.412
6 18.548 16.812 14.449 12.592 10.645 7.841 3.455 2.204 1.635 1.237 0.872 0.676
7 20.278 18.475 16.013 14.067 12.017 9.037 4.255 2.833 2.167 1.690 1.239 0.989
8 21.955 20.090 17.535 15.507 13.362 10.219 5.071 3.490 2.733 2.180 1.647 1.344
9 23.589 21.666 19.023 16.919 14.684 11.389 5.899 4.168 3.325 2.700 2.088 1.735
10 25.188 23.209 20.483 18.307 15.987 12.549 6.737 4.865 3.940 3.247 2.558 2.156
11 26.757 24.725 21.920 19.675 17.275 13.701 7.584 5.578 4.575 3.816 3.053 2.603
12 28.300 26.217 23.337 21.026 18.549 14.845 8.438 6.304 5.226 4.404 3.571 3.074
13 29.819 27.688 24.736 22.362 19.812 15.984 9.299 7.041 5.892 5.009 4.107 3.565
14 31.319 29.141 26.119 23.685 21.064 17.117 10.165 7.790 6.571 5.629 4.660 4.075
15 32.801 30.578 27.488 24.996 22.307 18.245 11.037 8.547 7.261 6.262 5.229 4.601
16 34.267 32.000 28.845 26.296 23.542 19.369 11.912 9.312 7.962 6.908 5.812 5.142
17 35.718 33.409 30.191 27.587 24.769 20.489 12.792 10.085 8.672 7.564 6.408 5.697
18 37.156 34.805 31.526 28.869 25.989 21.605 13.675 10.865 9.390 8.231 7.015 6.265
19 38.582 36.191 32.852 30.144 27.204 22.718 14.562 11.651 10.117 8.907 7.633 6.844
20 39.997 37.566 34.170 31.410 28.412 23.828 15.452 12.443 10.851 9.591 8.260 7.434
21 41.401 38.932 35.479 32.671 29.615 24.935 16.344 13.240 11.591 10.283 8.897 8.034
22 42.796 40.289 36.781 33.924 30.813 26.039 17.240 14.041 12.338 10.982 9.542 8.643
23 44.181 41.638 38.076 35.172 32.007 27.141 18.137 14.848 13.091 11.689 10.196 9.260
24 45.558 42.980 39.364 36.415 33.196 28.241 19.037 15.659 13.848 12.401 10.856 9.886
25 46.928 44.314 40.646 37.652 34.382 29.339 19.939 16.473 14.611 13.120 11.524 10.520
26 48.290 45.642 41.923 38.885 35.563 30.435 20.843 17.292 15.379 13.844 12.198 11.160
27 49.645 46.963 43.195 40.113 36.741 31.528 21.749 18.114 16.151 14.573 12.878 11.808
28 50.994 48.278 44.461 41.337 37.916 32.620 22.657 18.939 16.928 15.308 13.565 12.461
29 52.335 49.588 45.722 42.557 39.087 33.711 23.567 19.768 17.708 16.047 14.256 13.121
30 53.672 50.892 46.979 43.773 40.256 34.800 24.478 20.599 18.493 16.791 14.953 13.787
31 55.002 52.191 48.232 44.985 41.422 35.887 25.390 21.434 19.281 17.539 15.655 14.458
32 56.328 53.486 49.480 46.194 42.585 36.973 26.304 22.271 20.072 18.291 16.362 15.134
33 57.648 54.775 50.725 47.400 43.745 38.058 27.219 23.110 20.867 19.047 17.073 15.815
34 58.964 56.061 51.966 48.602 44.903 39.141 28.136 23.952 21.664 19.806 17.789 16.501
35 60.275 57.342 53.203 49.802 46.059 40.223 29.054 24.797 22.465 20.569 18.509 17.192
36 61.581 58.619 54.437 50.998 47.212 41.304 29.973 25.643 23.269 21.336 19.233 17.887
37 62.883 59.893 55.668 52.192 48.363 42.383 30.893 26.492 24.075 22.106 19.960 18.586
38 64.181 61.162 56.895 53.384 49.513 43.462 31.815 27.343 24.884 22.878 20.691 19.289
39 65.475 62.428 58.120 54.572 50.660 44.539 32.737 28.196 25.695 23.654 21.426 19.996
40 66.766 63.691 59.342 55.758 51.805 45.616 33.660 29.051 26.509 24.433 22.164 20.707
41 68.053 64.950 60.561 56.942 52.949 46.692 34.585 29.907 27.326 25.215 22.906 21.421
42 69.336 66.206 61.777 58.124 54.090 47.766 35.510 30.765 28.144 25.999 23.650 22.138
43 70.616 67.459 62.990 59.304 55.230 48.840 36.436 31.625 28.965 26.785 24.398 22.860
44 71.892 68.710 64.201 60.481 56.369 49.913 37.363 32.487 29.787 27.575 25.148 23.584
45 73.166 69.957 65.410 61.656 57.505 50.985 38.291 33.350 30.612 28.366 25.901 24.311
46 74.437 71.201 66.616 62.830 58.641 52.056 39.220 34.215 31.439 29.160 26.657 25.041
47 75.704 72.443 67.821 64.001 59.774 53.127 40.149 35.081 32.268 29.956 27.416 25.775
48 76.969 73.683 69.023 65.171 60.907 54.196 41.079 35.949 33.098 30.754 28.177 26.511
49 78.231 74.919 70.222 66.339 62.038 55.265 42.010 36.818 33.930 31.555 28.941 27.249
50 79.490 76.154 71.420 67.505 63.167 56.334 42.942 37.689 34.764 32.357 29.707 27.991
51 80.746 77.386 72.616 68.669 64.295 57.401 43.874 38.560 35.600 33.162 30.475 28.735
52 82.001 78.616 73.810 69.832 65.422 58.468 44.807 39.433 36.437 33.968 31.246 29.481
53 83.253 79.843 75.002 70.993 66.548 59.534 45.741 40.308 37.276 34.776 32.019 30.230
54 84.502 81.069 76.192 72.153 67.673 60.600 46.676 41.183 38.116 35.586 32.793 30.981
55 85.749 82.292 77.380 73.311 68.796 61.665 47.610 42.060 38.958 36.398 33.571 31.735
56 86.994 83.514 78.567 74.468 69.919 62.729 48.546 42.937 39.801 37.212 34.350 32.491
57 88.237 84.733 79.752 75.624 71.040 63.793 49.482 43.816 40.646 38.027 35.131 33.248
58 89.477 85.950 80.936 76.778 72.160 64.857 50.419 44.696 41.492 38.844 35.914 34.008
59 90.715 87.166 82.117 77.930 73.279 65.919 51.356 45.577 42.339 39.662 36.698 34.770
60 91.952 88.379 83.298 79.082 74.397 66.981 52.294 46.459 43.188 40.482 37.485 35.534
61 93.186 89.591 84.476 80.232 75.514 68.043 53.232 47.342 44.038 41.303 38.273 36.300
62 94.419 90.802 85.654 81.381 76.630 69.104 54.171 48.226 44.889 42.126 39.063 37.068
63 95.649 92.010 86.830 82.529 77.745 70.165 55.110 49.111 45.741 42.950 39.855 37.838
64 96.878 93.217 88.004 83.675 78.860 71.225 56.050 49.996 46.595 43.776 40.649 38.610
65 98.105 94.422 89.177 84.821 79.973 72.285 56.990 50.883 47.450 44.603 41.444 39.383
66 99.330 95.626 90.349 85.965 81.085 73.344 57.931 51.770 48.305 45.431 42.240 40.158
67 100.554 96.828 91.519 87.108 82.197 74.403 58.872 52.659 49.162 46.261 43.038 40.935
68 101.776 98.028 92.688 88.250 83.308 75.461 59.814 53.548 50.020 47.092 43.838 41.714
69 102.996 99.227 93.856 89.391 84.418 76.519 60.756 54.438 50.879 47.924 44.639 42.493
70 104.215 100.425 95.023 90.531 85.527 77.577 61.698 55.329 51.739 48.758 45.442 43.275
Valores críticos para la distribución χ2 para intervalos de confianza.
Niveles de confianza
gl 90 % 95 % 99 %
1 0.0039 3.8415 0.0010 5.0239 0.0000 7.8794
2 0.1026 5.9915 0.0506 7.3778 0.0100 10.5965
3 0.3518 7.8147 0.2158 9.3484 0.0717 12.8381
4 0.7107 9.4877 0.4844 11.1433 0.2070 14.8602
5 1.1455 11.0705 0.8312 12.8325 0.4118 16.7496
6 1.6354 12.5916 1.2373 14.4494 0.6757 18.5475
7 2.1673 14.0671 1.6899 16.0128 0.9893 20.2777
8 2.7326 15.5073 2.1797 17.5345 1.3444 21.9549
9 3.3251 16.9190 2.7004 19.0228 1.7349 23.5893
10 3.9403 18.3070 3.2470 20.4832 2.1558 25.1881
11 4.5748 19.6752 3.8157 21.9200 2.6032 26.7569
12 5.2260 21.0261 4.4038 23.3367 3.0738 28.2997
13 5.8919 22.3620 5.0087 24.7356 3.5650 29.8193
14 6.5706 23.6848 5.6287 26.1189 4.0747 31.3194
15 7.2609 24.9958 6.2621 27.4884 4.6009 32.8015
16 7.9616 26.2962 6.9077 28.8453 5.1422 34.2671
17 8.6718 27.5871 7.5642 30.1910 5.6973 35.7184
18 9.3904 28.8693 8.2307 31.5264 6.2648 37.1564
19 10.1170 30.1435 8.9065 32.8523 6.8439 38.5821
20 10.8508 31.4104 9.5908 34.1696 7.4338 39.9969
21 11.5913 32.6706 10.2829 35.4789 8.0336 41.4009
22 12.3380 33.9245 10.9823 36.7807 8.6427 42.7957
23 13.0905 35.1725 11.6885 38.0756 9.2604 44.1814
24 13.8484 36.4150 12.4011 39.3641 9.8862 45.5584
25 14.6114 37.6525 13.1197 40.6465 10.5196 46.9280
26 15.3792 38.8851 13.8439 41.9231 11.1602 48.2898
27 16.1514 40.1133 14.5734 43.1945 11.8077 49.6450
28 16.9279 41.3372 15.3079 44.4608 12.4613 50.9936
29 17.7084 42.5569 16.0471 45.7223 13.1211 52.3355
30 18.4927 43.7730 16.7908 46.9792 13.7867 53.6719
31 19.2806 44.9853 17.5387 48.2319 14.4577 55.0025
32 20.0719 46.1942 18.2908 49.4804 15.1340 56.3280
33 20.8665 47.3999 19.0467 50.7251 15.8152 57.6483
34 21.6643 48.6024 19.8062 51.9660 16.5013 58.9637
35 22.4650 49.8018 20.5694 53.2033 17.1917 60.2746
36 23.2686 50.9985 21.3359 54.4373 17.8868 61.5811
37 24.0749 52.1923 22.1056 55.6680 18.5859 62.8832
38 24.8839 53.3835 22.8785 56.8955 19.2888 64.1812
39 25.6954 54.5722 23.6543 58.1201 19.9958 65.4753
40 26.5093 55.7585 24.4331 59.3417 20.7066 66.7660
41 27.3256 56.9424 25.2145 60.5606 21.4208 68.0526
42 28.1440 58.1240 25.9987 61.7767 22.1384 69.3360
43 28.9647 59.3035 26.7854 62.9903 22.8596 70.6157
44 29.7875 60.4809 27.5745 64.2014 23.5836 71.8923
45 30.6123 61.6562 28.3662 65.4101 24.3110 73.1660
46 31.4390 62.8296 29.1600 66.6165 25.0413 74.4367
47 32.2676 64.0011 29.9562 67.8206 25.7745 75.7039
48 33.0981 65.1708 30.7545 69.0226 26.5107 76.9689
49 33.9303 66.3387 31.5549 70.2224 27.2494 78.2306
50 34.7642 67.5048 32.3574 71.4202 27.9908 79.4898
51 35.5999 68.6693 33.1618 72.6160 28.7347 80.7465
52 36.4371 69.8322 33.9681 73.8099 29.4811 82.0006
53 37.2759 70.9934 34.7763 75.0019 30.2300 83.2525
54 38.1162 72.1532 35.5863 76.1921 30.9811 84.5018
55 38.9581 73.3115 36.3981 77.3804 31.7349 85.7491
56 39.8013 74.4683 37.2116 78.5671 32.4906 86.9940
57 40.6459 75.6237 38.0267 79.7522 33.2482 88.2366
58 41.4920 76.7778 38.8435 80.9356 34.0085 89.4770
59 42.3393 77.9305 39.6619 82.1174 34.7704 90.7153
60 43.1880 79.0820 40.4817 83.2977 35.5344 91.9518
61 44.0379 80.2321 41.3032 84.4764 36.3005 93.1862
62 44.8890 81.3810 42.1260 85.6537 37.0683 94.4185
63 45.7414 82.5287 42.9503 86.8296 37.8383 95.6492
64 46.5949 83.6752 43.7759 88.0040 38.6097 96.8779
65 47.4496 84.8206 44.6030 89.1772 39.3832 98.1049
66 48.3054 85.9649 45.4314 90.3488 40.1583 99.3303
67 49.1623 87.1080 46.2610 91.5193 40.9349 100.5538
68 50.0203 88.2502 47.0919 92.6885 41.7136 101.7757
69 50.8792 89.3912 47.9241 93.8565 42.4934 102.9961
70 51.7393 90.5313 48.7575 95.0231 43.2753 104.2148
Valores críticos para la distribución t de Student
Valores de probabilidad acumulada Valores de probabilidad acumulada

gl 0.9000 0.9500 0.9750 0.9900 0.9950 gl 0.9000 0.9500 0.9750 0.9900 0.9950
1 3.0777 6.3137 12.7062 31.8210 63.6559 41 1.3025 1.6829 2.0195 2.4208 2.7012
2 1.8856 2.9200 4.3027 6.9645 9.9250 42 1.3020 1.6820 2.0181 2.4185 2.6981
3 1.6377 2.3534 3.1824 4.5407 5.8408 43 1.3016 1.6811 2.0167 2.4163 2.6951
4 1.5332 2.1318 2.7765 3.7469 4.6041 44 1.3011 1.6802 2.0154 2.4141 2.6923
5 1.4759 2.0150 2.5706 3.3649 4.0321 45 1.3007 1.6794 2.0141 2.4121 2.6896
6 1.4398 1.9432 2.4469 3.1427 3.7074 46 1.3002 1.6787 2.0129 2.4102 2.6870
7 1.4149 1.8946 2.3646 2.9979 3.4995 47 1.2998 1.6779 2.0117 2.4083 2.6846
8 1.3968 1.8595 2.3060 2.8965 3.3554 48 1.2994 1.6772 2.0106 2.4066 2.6822
9 1.3830 1.8331 2.2622 2.8214 3.2498 49 1.2991 1.6766 2.0096 2.4049 2.6800
10 1.3722 1.8125 2.2281 2.7638 3.1693 50 1.2987 1.6759 2.0086 2.4033 2.6778
11 1.3634 1.7959 2.2010 2.7181 3.1058 51 1.2984 1.6753 2.0076 2.4017 2.6757
12 1.3562 1.7823 2.1788 2.6810 3.0545 52 1.2980 1.6747 2.0066 2.4002 2.6737
13 1.3502 1.7709 2.1604 2.6503 3.0123 53 1.2977 1.6741 2.0057 2.3988 2.6718
14 1.3450 1.7613 2.1448 2.6245 2.9768 54 1.2974 1.6736 2.0049 2.3974 2.6700
15 1.3406 1.7531 2.1315 2.6025 2.9467 55 1.2971 1.6730 2.0040 2.3961 2.6682
16 1.3368 1.7459 2.1199 2.5835 2.9208 56 1.2969 1.6725 2.0032 2.3948 2.6665
17 1.3334 1.7396 2.1098 2.5669 2.8982 57 1.2966 1.6720 2.0025 2.3936 2.6649
18 1.3304 1.7341 2.1009 2.5524 2.8784 58 1.2963 1.6716 2.0017 2.3924 2.6633
19 1.3277 1.7291 2.0930 2.5395 2.8609 59 1.2961 1.6711 2.0010 2.3912 2.6618
20 1.3253 1.7247 2.0860 2.5280 2.8453 60 1.2958 1.6706 2.0003 2.3901 2.6603
21 1.3232 1.7207 2.0796 2.5176 2.8314 61 1.2956 1.6702 1.9996 2.3890 2.6589
22 1.3212 1.7171 2.0739 2.5083 2.8188 62 1.2954 1.6698 1.9990 2.3880 2.6575
23 1.3195 1.7139 2.0687 2.4999 2.8073 63 1.2951 1.6694 1.9983 2.3870 2.6561
24 1.3178 1.7109 2.0639 2.4922 2.7970 64 1.2949 1.6690 1.9977 2.3860 2.6549
25 1.3163 1.7081 2.0595 2.4851 2.7874 65 1.2947 1.6686 1.9971 2.3851 2.6536
26 1.3150 1.7056 2.0555 2.4786 2.7787 66 1.2945 1.6683 1.9966 2.3842 2.6524
27 1.3137 1.7033 2.0518 2.4727 2.7707 67 1.2943 1.6679 1.9960 2.3833 2.6512
28 1.3125 1.7011 2.0484 2.4671 2.7633 68 1.2941 1.6676 1.9955 2.3824 2.6501
29 1.3114 1.6991 2.0452 2.4620 2.7564 69 1.2939 1.6672 1.9949 2.3816 2.6490
30 1.3104 1.6973 2.0423 2.4573 2.7500 70 1.2938 1.6669 1.9944 2.3808 2.6479
31 1.3095 1.6955 2.0395 2.4528 2.7440 71 1.2936 1.6666 1.9939 2.3800 2.6469
32 1.3086 1.6939 2.0369 2.4487 2.7385 72 1.2934 1.6663 1.9935 2.3793 2.6458
33 1.3077 1.6924 2.0345 2.4448 2.7333 73 1.2933 1.6660 1.9930 2.3785 2.6449
34 1.3070 1.6909 2.0322 2.4411 2.7284 74 1.2931 1.6657 1.9925 2.3778 2.6439
35 1.3062 1.6896 2.0301 2.4377 2.7238 75 1.2929 1.6654 1.9921 2.3771 2.6430
36 1.3055 1.6883 2.0281 2.4345 2.7195 76 1.2928 1.6652 1.9917 2.3764 2.6421
37 1.3049 1.6871 2.0262 2.4314 2.7154 77 1.2926 1.6649 1.9913 2.3758 2.6412
38 1.3042 1.6860 2.0244 2.4286 2.7116 78 1.2925 1.6646 1.9908 2.3751 2.6403
39 1.3036 1.6849 2.0227 2.4258 2.7079 79 1.2924 1.6644 1.9905 2.3745 2.6395
40 1.3031 1.6839 2.0211 2.4233 2.7045 80 1.2922 1.6641 1.9901 2.3739 2.6387

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X ∼ B(n, p) P (X ≤ x)

P (Z < z) z P (Z < z) z P (Z < z) z P (Z < z) z P (Z < z) z P (Z < z) z P (Z < z) z

Valores de probabilidad anti-acumulada

Valores de probabilidad acumulada Valores de probabilidad acumulada

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