Do not write in this booklet

Statistical
Tables
A: Cumulative Binomial tables

b: cumulative poisson tables

c: standard normal tables

d: cumulative t tables

e: Chi-squared tables
f: f distribution tables
Table A.1 Cumulative Binomial Distribution

𝒏 𝒙 𝒑 = 𝟎. 𝟏 𝒑 = 𝟎. 𝟐 𝒑 = 𝟎. 𝟐𝟓 𝒑 = 𝟎. 𝟑 𝒑 = 𝟏⁄𝟑 𝒑 = 𝟎. 𝟒 𝒑 = 𝟎. 𝟓 𝒑 = 𝟎. 𝟔 𝒑 = 𝟐⁄𝟑 𝒑 = 𝟎. 𝟕 𝒑 = 𝟎. 𝟕𝟓 𝒑 = 𝟎. 𝟖 𝒑 = 𝟎. 𝟗

7 0 0.4783 0.2097 0.1335 0.0824 0.0585 0.0280 0.0078 0.0016 0.0005 0.0002 0.0001 0.0000 0.0000
7 1 0.8503 0.5767 0.4449 0.3294 0.2634 0.1586 0.0625 0.0188 0.0069 0.0038 0.0013 0.0004 0.0000
7 2 0.9743 0.8520 0.7564 0.6471 0.5707 0.4199 0.2266 0.0963 0.0452 0.0288 0.0129 0.0047 0.0002
7 3 0.9973 0.9667 0.9294 0.8740 0.8268 0.7102 0.5000 0.2898 0.1732 0.1260 0.0706 0.0333 0.0027
7 4 0.9998 0.9953 0.9871 0.9712 0.9548 0.9037 0.7734 0.5801 0.4293 0.3529 0.2436 0.1480 0.0257
7 5 1.0000 0.9996 0.9987 0.9962 0.9931 0.9812 0.9375 0.8414 0.7366 0.6706 0.5551 0.4233 0.1497
7 6 1.0000 1.0000 0.9999 0.9998 0.9995 0.9984 0.9922 0.9720 0.9415 0.9176 0.8665 0.7903 0.5217
7 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

𝒏 𝒙 𝒑 = 𝟎. 𝟏 𝒑 = 𝟎. 𝟐 𝒑 = 𝟎. 𝟐𝟓 𝒑 = 𝟎. 𝟑 𝒑 = 𝟏⁄𝟑 𝒑 = 𝟎. 𝟒 𝒑 = 𝟎. 𝟓 𝒑 = 𝟎. 𝟔 𝒑 = 𝟐⁄𝟑 𝒑 = 𝟎. 𝟕 𝒑 = 𝟎. 𝟕𝟓 𝒑 = 𝟎. 𝟖 𝒑 = 𝟎. 𝟗
8 0 0.4305 0.1678 0.1001 0.0576 0.0390 0.0168 0.0039 0.0007 0.0002 0.0001 0.0000 0.0000 0.0000
8 1 0.8131 0.5033 0.3671 0.2553 0.1951 0.1064 0.0352 0.0085 0.0026 0.0013 0.0004 0.0001 0.0000
8 2 0.9619 0.7969 0.6785 0.5518 0.4683 0.3154 0.1445 0.0498 0.0197 0.0113 0.0042 0.0012 0.0000
8 3 0.9950 0.9437 0.8862 0.8059 0.7414 0.5941 0.3633 0.1737 0.0879 0.0580 0.0273 0.0104 0.0004
8 4 0.9996 0.9896 0.9727 0.9420 0.9111 0.8163 0.6367 0.4059 0.2586 0.1941 0.1138 0.0563 0.0050
8 5 1.0000 0.9988 0.9958 0.9887 0.9803 0.9502 0.8555 0.6846 0.5317 0.4481 0.3215 0.2031 0.0381
8 6 1.0000 0.9999 0.9996 0.9987 0.9974 0.9915 0.9648 0.8936 0.8049 0.7447 0.6329 0.4967 0.1869
8 7 1.0000 1.0000 1.0000 0.9999 0.9993 0.9993 0.9961 0.9832 0.9610 0.9424 0.8999 0.8321 0.5695
8 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

𝒏 𝒙 𝒑 = 𝟎. 𝟏 𝒑 = 𝟎. 𝟐 𝒑 = 𝟎. 𝟐𝟓 𝒑 = 𝟎. 𝟑 𝒑 = 𝟏⁄𝟑 𝒑 = 𝟎. 𝟒 𝒑 = 𝟎. 𝟓 𝒑 = 𝟎. 𝟔 𝒑 = 𝟐⁄𝟑 𝒑 = 𝟎. 𝟕 𝒑 = 𝟎. 𝟕𝟓 𝒑 = 𝟎. 𝟖 𝒑 = 𝟎. 𝟗
9 0 0.3874 0.1342 0.0751 0.0404 0.0260 0.0101 0.0020 0.0003 0.0001 0.0000 0.0000 0.0000 0.0000
9 1 0.7748 0.4361 0.3003 0.1960 0.1431 0.0705 0.0195 0.0038 0.0010 0.0004 0.0001 0.0000 0.0000
9 2 0.9470 0.7382 0.6007 0.4628 0.3773 0.1318 0.0898 0.0250 0.0083 0.0043 0.0013 0.0003 0.0000
9 3 0.9917 0.9144 0.8343 0.7297 0.6504 0.4826 0.2539 0.0994 0.0424 0.0253 0.0100 0.0031 0.0001
9 4 0.9991 0.9804 0.9511 0.9012 0.8552 0.7334 0.5000 0.2666 0.1448 0.0988 0.0489 0.0196 0.0009
9 5 0.9999 0.9969 0.9900 0.9747 0.9576 0.9006 0.7461 0.5174 0.3496 0.2703 0.1657 0.0856 0.0083
9 6 1.0000 0.9997 0.9987 0.9957 0.9917 0.9750 0.9102 0.7682 0.6227 0.5372 0.3993 0.2618 0.0530
9 7 1.0000 1.0000 0.9999 0.9996 0.9990 0.9962 0.9805 0.9295 0.8569 0.8040 0.6997 0.5638 0.2252
9 8 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9980 0.9899 0.9740 0.9596 0.9249 0.8658 0.6126
9 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
Table A.2 Cumulative Binomial Distribution…

𝒏 𝒙 𝒑 = 𝟎. 𝟏 𝒑 = 𝟎. 𝟐 𝒑 = 𝟎. 𝟐𝟓 𝒑 = 𝟎. 𝟑 𝒑 = 𝟏⁄𝟑 𝒑 = 𝟎. 𝟒 𝒑 = 𝟎. 𝟓 𝒑 = 𝟎. 𝟔 𝒑 = 𝟐⁄𝟑 𝒑 = 𝟎. 𝟕 𝒑 = 𝟎. 𝟕𝟓 𝒑 = 𝟎. 𝟖 𝒑 = 𝟎. 𝟗

10 0 0.34870 0.10740 0.05630 0.02820 0.01740 0.00600 0.00100 0.00010 0.00000 0.00000 0.00000 0.00000 0.00000
10 1 0.73610 0.37580 0.24400 0.14930 0.10410 0.04640 0.01070 0.00170 0.00040 0.00010 0.00000 0.00000 0.00000
10 2 0.92980 0.67780 0.52560 0.38280 0.29920 0.16730 0.05470 0.01230 0.00340 0.00160 0.00040 0.00010 0.00000
10 3 0.98720 0.87910 0.77590 0.64960 0.55940 0.38230 0.17190 0.05480 0.01970 0.01060 0.00350 0.00090 0.00000
10 4 0.99840 0.96720 0.92190 0.84970 0.78690 0.63310 0.37700 0.16620 0.07650 0.04730 0.01970 0.00640 0.00010
10 5 0.99990 0.99360 0.98030 0.95270 0.92350 0.83380 0.62300 0.36690 0.21310 0.15030 0.07810 0.03280 0.00160
10 6 1.00000 0.99910 0.99650 0.98940 0.98030 0.94520 0.82810 0.61770 0.44060 0.35040 0.22410 0.12090 0.01280
10 7 1.00000 0.99990 0.99960 0.99840 0.99660 0.98770 0.94530 0.83270 0.70080 0.61720 0.47440 0.32220 0.07020
10 8 1.00000 1.00000 1.00000 0.99990 0.99960 0.99830 0.98930 0.95360 0.89590 0.85070 0.75600 0.62420 0.26390
10 9 1.00000 1.00000 1.00000 1.00000 1.00000 0.99990 0.99900 0.99400 0.98260 0.97180 0.94370 0.89260 0.65130
10 10 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000

𝒏 𝒙 𝒑 = 𝟎. 𝟏 𝒑 = 𝟎. 𝟐 𝒑 = 𝟎. 𝟐𝟓 𝒑 = 𝟎. 𝟑 𝒑 = 𝟏⁄𝟑 𝒑 = 𝟎. 𝟒 𝒑 = 𝟎. 𝟓 𝒑 = 𝟎. 𝟔 𝒑 = 𝟐⁄𝟑 𝒑 = 𝟎. 𝟕 𝒑 = 𝟎. 𝟕𝟓 𝒑 = 𝟎. 𝟖 𝒑 = 𝟎. 𝟗
11 0 0.31380 0.08590 0.04220 0.01980 0.01160 0.00360 0.00050 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
11 1 0.69740 0.32210 0.19710 0.11300 0.07520 0.03020 0.00590 0.00070 0.00010 0.00000 0.00000 0.00000 0.00000
11 2 0.91040 0.61740 0.45520 0.31270 0.23420 0.11890 0.03270 0.00590 0.00140 0.00060 0.00010 0.00000 0.00000
11 3 0.98150 0.83890 0.71330 0.56960 0.47270 0.29630 0.11330 0.02930 9.00880 0.00430 0.00120 0.00020 0.00000
11 4 0.99720 0.94960 0.88540 0.78970 0.71110 0.53280 0.27440 0.09940 0.03860 0.02160 0.00760 0.00200 0.00000
11 5 0.99970 0.98830 0.96570 0.92180 0.87800 0.75350 0.50000 0.24650 0.12200 0.07820 0.03430 0.01170 0.00030
11 6 1.00000 0.99800 0.99240 0.97840 0.96140 0.90060 .0.7256 0.46720 0.28890 0.21030 0.11460 0.05040 0.00280
11 7 1.00000 0.99980 0.99880 0.99570 0.99120 0.97070 0.88670 0.70370 0.52730 0.43040 0.28670 0.16110 0.01850
11 8 1.00000 1.00000 0.99990 0.999.4 0.99860 0.99410 0.96730 0.88110 0.76580 0.68730 0.54480 0.38260 0.08960
11 9 1.00000 1.00000 1.00000 1.00000 0.99990 0.99930 0.99410 0.96980 0.92480 0.88700 0.80290 0.67790 0.30260
11 10 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 0.99950 0.99640 0.98840 0.98020 0.95780 0.91410 0.68620
11 11 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
Table A.3 Cumulative Binomial Distribution…

𝒏 𝒙 𝒑 = 𝟎. 𝟏 𝒑 = 𝟎. 𝟐 𝒑 = 𝟎. 𝟐𝟓 𝒑 = 𝟎. 𝟑 𝒑 = 𝟏⁄𝟑 𝒑 = 𝟎. 𝟒 𝒑 = 𝟎. 𝟓 𝒑 = 𝟎. 𝟔 𝒑 = 𝟐⁄𝟑 𝒑 = 𝟎. 𝟕 𝒑 = 𝟎. 𝟕𝟓 𝒑 = 𝟎. 𝟖 𝒑 = 𝟎. 𝟗

12 0 0.28240 0.06870 0.03170 0.01380 0.00770 0.00220 0.00020 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
12 1 0.65900 0.27490 0.15840 0.08500 0.05400 0.01960 0.00320 0.00030 0.00000 0.00000 0.00000 0.00000 0.00000
12 2 0.88910 0.55830 0.39070 0.25280 0.18120 0.08340 0.01930 0.00280 0.00050 0.00020 0.00000 0.00000 0.00000
12 3 0.97440 0.79460 0.64880 0.49250 0.39320 0.22530 0.07300 0.01530 0.00390 0.00170 0.00040 0.00010 0.00000
12 4 0.99570 0.92740 0.84240 0.72370 0.63160 0.43820 0.19380 0.05730 0.01870 0.00950 0.00280 0.00060 0.00000
12 5 6.94097 0.98060 0.94560 0.88220 0.82230 0.66520 0.38720 0.15820 0.06640 0.03860 0.01430 0.00390 0.00010
12 6 0.99990 0.99610 0.98570 0.96140 0.93360 0.84180 0.61280 0.33480 0.17770 0.11780 0.05440 0.01940 0.00050
12 7 1.00000 0.99940 0.99720 0.99050 0.98130 0.94270 0.80620 0.56180 0.36840 0.27630 0.15760 0.07260 0.00430
12 8 1.00000 0.99990 0.99960 0.99830 0.99610 0.98470 0.92700 0.77470 0.60680 0.50750 0.35120 0.20540 0.02560
12 9 1.00000 1.00000 1.00000 0.99980 0.99950 0.99720 0.98070 0.91660 0.81880 0.74720 0.60930 0.44170 0.11090
12 10 1.00000 1.00000 1.00000 1.00000 1.00000 0.99970 0.99680 0.98040 0.94600 0.91500 0.84160 0.72510 0.34100
12 11 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 0.99980 0.99780 0.99230 0.98620 0.96830 0.93130 0.71760
12 12 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000

𝒏 𝒙 𝒑 = 𝟎. 𝟏 𝒑 = 𝟎. 𝟐 𝒑 = 𝟎. 𝟐𝟓 𝒑 = 𝟎. 𝟑 𝒑 = 𝟏⁄𝟑 𝒑 = 𝟎. 𝟒 𝒑 = 𝟎. 𝟓 𝒑 = 𝟎. 𝟔 𝒑 = 𝟐⁄𝟑 𝒑 = 𝟎. 𝟕 𝒑 = 𝟎. 𝟕𝟓 𝒑 = 𝟎. 𝟖 𝒑 = 𝟎. 𝟗
13 0 0.2542 0.0550 0.0238 0.0097 0.0051 0.0013 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
13 1 0.6213 0.2336 0.1267 0.0637 0.0386 0.0126 0.0017 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000
13 2 0.8661 0.5017 0.3326 0.2025 0.1388 0.0579 0.0112 0.0013 0.0002 0.0001 0.0000 0.0000 0.0000
13 3 0.9658 0.7473 0.5843 0.4206 0.3225 0.1686 0.0461 0.0078 0.0016 0.0700 0.0001 0.0000 0.0000
13 4 0.9935 0.9009 0.7940 0.6543 0.5521 0.3530 0.1334 0.0321 0.0088 0.0040 0.0010 0.0002 0.0000
13 5 0.9991 0.9700 0.9198 0.8346 0.7588 0.5744 0.2905 0.0977 0.0346 0.0182 0.0056 0.0012 0.0000
13 6 0.9999 0.9930 0.9757 0.9376 0.8965 0.7712 0.5000 0.2288 0.1035 0.0624 0.0243 0.0070 0.0001
13 7 1.0000 0.9988 0.9944 0.9818 0.9654 0.9023 0.7095 0.4156 0.2412 0.1654 0.0802 0.0300 0.0009
13 8 1.0000 0.9998 0.9990 0.9960 0.9912 0.9679 0.8666 0.6470 0.4479 0.3457 0.2060 0.0991 0.0065
13 9 1.0000 1.0000 0.9999 0.9993 0.9984 0.9922 0.9539 0.8314 0.6775 0.5794 0.4157 0.2527 0.0342
13 10 1.0000 1.0000 1.0000 0.9999 0.9998 0.9987 0.9888 0.9421 0.8612 0.7975 0.6674 0.4983 0.1339
13 11 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9983 0.9874 0.9614 0.9363 0.8733 0.7664 0.3787
13 12 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9987 0.9949 0.9903 0.9762 0.9450 0.7458
13 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
Table A.4 Cumulative Binomial Distribution…

𝒏 𝒙 𝒑 = 𝟎. 𝟏 𝒑 = 𝟎. 𝟐 𝒑 = 𝟎. 𝟐𝟓 𝒑 = 𝟎. 𝟑 𝒑 = 𝟏⁄𝟑 𝒑 = 𝟎. 𝟒 𝒑 = 𝟎. 𝟓 𝒑 = 𝟎. 𝟔 𝒑 = 𝟐⁄𝟑 𝒑 = 𝟎. 𝟕 𝒑 = 𝟎. 𝟕𝟓 𝒑 = 𝟎. 𝟖 𝒑 = 𝟎. 𝟗
14 0 0.2288 0.0440 0.0178 0.0068 0.0034 0.0008 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
14 1 0.5846 0.1979 0.1010 0.0475 0.0274 0.0081 0.0009 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000
14 2 0.8416 0.4481 0.2811 0.1608 0.1054 0.0398 0.0065 0.0006 0.0001 0.0000 0.0000 0.0000 0.0000
14 3 0.9559 0.6982 0.5213 0.3552 0.2613 0.1243 0.0287 0.0039 0.0007 0.0002 0.0000 0.0000 0.0000
14 4 0.9908 0.8702 0.7415 0.5842 0.4756 0.2793 0.0898 0.0175 0.0040 0.0017 0.0003 0.0000 0.0000
14 5 0.9985 0.9561 0.8883 0.7805 0.6899 0.4859 0.2120 0.0583 0.0174 0.0083 0.0022 0.0004 0.0000
14 6 0.9998 0.9884 0.9617 0.9067 0.8506 0.6925 0.3953 0.1501 0.0576 0.0315 0.0103 0.0024 0.0000
14 7 1.0000 0.9976 0.9897 0.9685 0.9424 0.8499 0.6047 0.3075 0.1494 0.0933 0.0383 0.0116 0.0002
14 8 1.0000 0.9996 0.9978 0.9917 0.9816 0.9417 0.7880 0.5141 0.3101 0.2195 0.1117 0.0439 0.0015
14 9 1.0000 1.0000 0.9997 0.9983 0.9960 0.9825 0.9102 0.7207 0.5244 0.4158 0.2585 0.1298 0.0092
14 10 1.0000 1.0000 1.0000 0.9998 0.9993 0.9961 0.9713 0.8757 0.7387 0.6448 0.4787 0.3018 0.0441
14 11 1.0000 1.0000 1.0000 1.0000 0.9999 0.9994 0.9935 0.9602 0.8946 0.8392 0.7189 0.5519 0.1584
14 12 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9991 0.9919 0.9726 0.9525 0.8990 0.8021 0.4154
14 13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9992 0.9966 0.9932 0.9822 0.9560 0.7712
14 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

𝒏 𝒙 𝒑 = 𝟎. 𝟏 𝒑 = 𝟎. 𝟐 𝒑 = 𝟎. 𝟐𝟓 𝒑 = 𝟎. 𝟑 𝒑 = 𝟏⁄𝟑 𝒑 = 𝟎. 𝟒 𝒑 = 𝟎. 𝟓 𝒑 = 𝟎. 𝟔 𝒑 = 𝟐⁄𝟑 𝒑 = 𝟎. 𝟕 𝒑 = 𝟎. 𝟕𝟓 𝒑 = 𝟎. 𝟖 𝒑 = 𝟎. 𝟗
15 0 0.2059 0.0352 0.0134 0.0047 0.0023 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
15 1 0.5490 0.1671 0.0802 0.0353 0.0194 0.0052 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
15 2 0.8159 0.3980 0.2361 0.1268 0.0794 0.0271 0.0037 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000
15 3 0.9444 0.6482 0.4613 0.2969 0.2093 0.0905 0.0176 0.0019 0.0003 0.0001 0.0000 0.0000 0.0000
15 4 0.9873 0.8358 0.6865 0.5155 0.4042 0.2173 0.0592 0.0093 0.0018 0.0007 0.0001 0.0000 0.0000
15 5 0.9978 0.9389 0.8516 0.7216 0.6185 0.4032 0.1509 0.0338 0.0085 0.0037 0.0008 0.0001 0.0000
15 6 0.9997 0.9819 0.9434 0.8689 0.7970 0.6098 0.3036 0.0950 0.0308 0.0152 0.0042 0.0008 0.0000
15 7 1.0000 0.9958 0.9827 0.9500 0.9118 0.7869 0.5000 0.2131 0.0882 0.0500 0.0173 0.0042 0.0000
15 8 1.0000 0.9992 0.9958 0.9848 0.9692 0.9050 0.6964 0.3902 0.2030 0.1311 0.0566 0.0181 0.0003
15 9 1.0000 0.9999 0.9992 0.9963 0.9915 0.9662 0.8491 0.5968 0.3815 0.2784 0.1484 0.0611 0.0022
15 10 1.0000 1.0000 0.9999 0.9993 0.9982 0.9907 0.9408 0.7827 0.5958 0.4845 0.3135 0.1642 0.0127
15 11 1.0000 1.0000 1.0000 0.9999 0.9997 0.9981 0.9824 0.9095 0.7907 0.7031 0.5387 0.3518 0.0556
15 12 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9963 0.9729 0.9206 0.8732 0.7639 0.6020 0.1841
15 13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9948 0.9806 0.9647 0.9198 0.8329 0.4510
15 14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9977 0.9953 0.9866 0.9648 0.7941
15 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
Table A.5 Cumulative Binomial Distribution…

𝒏 𝒙 𝒑 = 𝟎. 𝟏 𝒑 = 𝟎. 𝟐 𝒑 = 𝟎. 𝟐𝟓 𝒑 = 𝟎. 𝟑 𝒑 = 𝟏⁄𝟑 𝒑 = 𝟎. 𝟒 𝒑 = 𝟎. 𝟓 𝒑 = 𝟎. 𝟔 𝒑 = 𝟐⁄𝟑 𝒑 = 𝟎. 𝟕 𝒑 = 𝟎. 𝟕𝟓 𝒑 = 𝟎. 𝟖 𝒑 = 𝟎. 𝟗

16 0 0.1853 0.0281 0.0100 0.0033 0.0015 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
16 1 0.5147 0.1407 0.0635 0.0261 0.0137 0.0033 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
16 2 0.7892 0.3518 0.1971 0.0994 0.0594 0.0183 0.0021 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000
16 3 0.9316 0.5981 0.4050 0.2459 0.1660 0.0651 0.0106 0.0009 0.0001 0.0000 0.0000 0.0000 0.0000
16 4 0.9830 0.7982 0.6302 0.4499 0.3392 0.1666 0.0384 0.0049 0.0008 0.0003 0.0000 0.0000 0.0000
16 5 0.9967 0.9183 0.8103 0.6598 0.5471 0.3288 0.1051 0.0191 0.0040 0.0016 0.0003 0.0000 0.0000
16 6 0.9995 0.9733 0.9204 0.8247 0.7375 0.5272 0.2272 0.0583 0.0159 0.0071 0.0016 0.0002 0.0000
16 7 0.9999 0.9930 0.9729 0.9256 0.8736 0.7161 0.4018 0.1423 0.0499 0.0257 0.0075 0.0015 0.0000
16 8 1.0000 0.9985 0.9925 0.9743 0.9501 0.8577 0.5982 0.2839 0.1264 0.0744 0.0271 0.0070 0.0001
16 9 1.0000 0.9998 0.9984 0.9929 0.9841 0.9417 0.7728 0.4728 0.2625 0.1753 0.0796 0.0267 0.0005
16 10 1.0000 1.0000 0.9997 0.9984 0.9960 0.9809 0.8949 0.6712 0.4529 0.3402 0.1897 0.0817 0.0033
16 11 1.0000 1.0000 1.0000 0.9997 0.9992 0.9951 0.9616 0.8334 0.6608 0.5501 0.3698 0.2018 0.0170
16 12 1.0000 1.0000 1.0000 1.0000 0.9999 0.9991 0.9894 0.9349 0.8340 0.7541 0.5950 0.4019 0.0684
16 13 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9979 0.9817 0.9406 0.9006 0.8029 0.6482 0.2108
16 14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9967 0.9863 0.9739 0.9365 0.8593 0.4853
16 15 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9985 0.9967 0.9900 0.9719 0.8147
16 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
Table A.6 Cumulative Binomial Distribution…

𝒏 𝒙 𝒑 = 𝟎. 𝟏 𝒑 = 𝟎. 𝟐 𝒑 = 𝟎. 𝟐𝟓 𝒑 = 𝟎. 𝟑 𝒑 = 𝟏⁄𝟑 𝒑 = 𝟎. 𝟒 𝒑 = 𝟎. 𝟓 𝒑 = 𝟎. 𝟔 𝒑 = 𝟐⁄𝟑 𝒑 = 𝟎. 𝟕 𝒑 = 𝟎. 𝟕𝟓 𝒑 = 𝟎. 𝟖 𝒑 = 𝟎. 𝟗

17 0 0.1668 0.0225 0.0075 0.0013 0.0010 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
17 1 0.4818 0.1182 0.0501 0.0193 0.0096 0.0011 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
17 2 0.7618 0.3096 0.1637 0.0774 0.0442 0.0123 0.0012 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000
17 3 0.9174 0.5489 0.3530 0.2019 0.1305 0.0464 0.0064 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000
17 4 0.9779 0.7582 0.5739 0.3887 0.2815 0.1160 0.0245 0.0025 0.0003 0.0001 0.0000 0.0000 0.0000
17 5 0.9953 0.8943 0.7653 0.5968 0.4778 0.1639 0.0717 0.0106 0.0019 0.0007 0.0001 0.0000 0.0000
17 6 0.9991 0.9613 0.8919 0.7752 0.6740 0.4478 0.1661 0.0348 0.0080 0.0032 0.0006 0.0001 0.0000
17 7 0.9999 0.9891 0.9598 0.8954 0.8282 0.6405 0.3145 0.0919 0.0273 0.0127 0.0031 0.0005 0.0000
17 8 1.0000 0.9914 0.9876 0.9597 0.9246 0.8011 0.5000 0.1989 0.0754 0.0403 0.0124 0.0026 0.0000
17 9 1.0000 0.9995 0.9969 0.9873 0.9727 0.9081 0.6855 0.3595 0.1718 0.1046 0.0402 0.0109 0.0001
17 10 1.0000 0.9999 0.9994 0.9968 0.9920 0.9652 0.8338 0.5522 0.3260 0.2248 0.1071 0.0377 0.0008
17 11 1.0000 1.0000 0.9999 0.9993 0.9981 0.9894 0.9283 0.7361 0.5222 0.4031 0.2347 0.1057 0.0047
17 12 1.0000 1.0000 1.0000 0.9999 0.9997 0.9975 0.9755 0.8740 0.7185 0.6113 0.4261 0.2418 0.0221
17 13 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9936 0.9536 0.8695 0.7981 0.6470 0.4511 0.0826
17 14 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9988 0.9877 0.9558 0.9226 0.8363 0.6904 0.2381
17 15 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9979 0.9904 0.9807 0.9499 0.8818 0.5181
17 16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9990 0.9977 0.9925 0.9775 0.8332
17 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
Table A.7 Cumulative Binomial Distribution…

𝒏 𝒙 𝒑 = 𝟎. 𝟏 𝒑 = 𝟎. 𝟐 𝒑 = 𝟎. 𝟐𝟓 𝒑 = 𝟎. 𝟑 𝒑 = 𝟏⁄𝟑 𝒑 = 𝟎. 𝟒 𝒑 = 𝟎. 𝟓 𝒑 = 𝟎. 𝟔 𝒑 = 𝟐⁄𝟑 𝒑 = 𝟎. 𝟕 𝒑 = 𝟎. 𝟕𝟓 𝒑 = 𝟎. 𝟖 𝒑 = 𝟎. 𝟗

18 0 0.1501 0.0180 0.0056 0.0016 0.0007 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
18 1 0.4503 0.0991 0.0395 0.0142 0.0068 0.0013 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
18 2 0.7338 0.2713 0.1353 0.0600 0.0327 0.0082 0.0007 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
18 3 0.9018 0.5010 0.3057 0.1646 0.1017 0.0318 0.0038 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000
18 4 0.9718 0.7164 0.5187 0.3327 0.1312 0.0942 0.0154 0.0013 0.0001 0.0000 0.0000 0.0000 0.0000
18 5 0.9936 0.8671 0.7175 0.5344 0.4124 0.2088 0.0481 0.0058 0.0009 0.0003 0.0000 0.0000 0.0000
18 6 0.9988 0.9487 0.8610 0.7217 0.6086 0.3743 0.1189 0.0203 0.0039 0.0014 0.0002 0.0000 0.0000
18 7 0.9998 0.9837 0.9431 0.8593 0.7768 0.5634 0.2403 0.0576 0.0144 0.0061 0.0012 0.0002 0.0000
18 8 1.0000 0.9957 0.9807 0.9404 0.8925 0.1368 0.4073 0.1347 0.0433 0.0210 0.0054 0.0009 0.0000
18 9 1.0000 0.9991 0.9946 0.9790 0.9567 0.8653 0.5917 0.2632 0.1075 0.0596 0.0193 0.0043 0.0000
18 10 1.0000 0.9998 0.9988 0.9939 0.9856 0.9414 0.7597 0.4366 0.2132 0.1407 0.0569 0.0163 0.0002
18 11 1.0000 1.0000 0.9998 0.9986 0.9961 0.9797 0.8811 0.6157 0.3914 0.2783 0.1390 0.0513 0.0012
18 12 1.0000 1.0000 1.0000 0.9997 0.9991 0.9942 0.9519 0.7912 0.5876 0.4656 0.2825 0.1329 0.0064
18 13 1.0000 1.0000 1.0000 1.0000 0.9999 0.9987 0.9846 0.9058 0.7688 0.6673 0.4813 0.2836 0.0282
18 14 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9962 0.9672 0.8983 0.8354 0.6943 0.4990 0.0982
18 15 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9993 0.9918 0.9673 0.9400 0.8647 0.7287 0.2662
18 16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9987 0.9931 0.9858 0.9605 0.9009 9.5497
18 17 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9993 0.9984 0.9944 0.9820 0.8499
18 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
Table A.8 Cumulative Binomial Distribution…

𝒏 𝒙 𝒑 = 𝟎. 𝟏 𝒑 = 𝟎. 𝟐 𝒑 = 𝟎. 𝟐𝟓 𝒑 = 𝟎. 𝟑 𝒑 = 𝟏⁄𝟑 𝒑 = 𝟎. 𝟒 𝒑 = 𝟎. 𝟓 𝒑 = 𝟎. 𝟔 𝒑 = 𝟐⁄𝟑 𝒑 = 𝟎. 𝟕 𝒑 = 𝟎. 𝟕𝟓 𝒑 = 𝟎. 𝟖 𝒑 = 𝟎. 𝟗

19 0 0.1351 0.0144 0.0042 0.0011 0.0005 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
19 1 0.4203 0.0829 0.0310 0.0104 0.0047 0.0008 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
19 2 0.7054 0.2369 0.1113 0.0462 0.0240 0.0055 0.0004 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
19 3 0.8850 0.4551 0.2631 0.1332 0.0787 0.0210 0.0022 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000
19 4 0.9648 0.6733 0.4654 0.2822 0.1880 0.0696 0.0096 0.0006 0.0001 0.0000 0.0000 0.0000 0.0000
19 5 0.9914 0.8369 0.6678 0.4139 0.3520 0.1629 0.0318 0.0031 0.0004 0.0001 0.0000 0.0000 0.0000
19 6 0.9983 0.9314 0.8251 0.6655 0.5432 0.3081 0.0835 0.0116 0.0019 0.0006 0.0001 0.0000 0.0000
19 7 0.9997 0.9767 0.9225 0.8180 0.7208 0.4878 0.1796 0.0352 0.0074 0.0028 0.0005 0.0000 0.0000
19 8 1.0000 0.9933 0.9713 0.9161 0.8539 0.6675 0.3238 0.0885 0.0241 0.0105 0.0023 0.0003 0.0000
19 9 1.0000 0.9984 0.9911 0.9674 0.9353 0.8139 0.5000 0.1861 0.0647 0.0326 0.0089 0.0016 0.0000
19 10 1.0000 0.9997 0.9977 0.9895 0.9759 0.9115 0.6762 0.3325 0.1461 0.0839 0.0287 0.0067 0.0000
19 11 1.0000 1.0000 0.9995 0.9972 0.9926 0.9648 0.8204 0.5122 0.2792 0.1820 0.0775 0.0233 0.0003
19 12 1.0000 1.0000 0.9999 0.9994 0.9981 0.9884 0.9165 0.6919 0.4568 0.3345 0.1749 0.0676 0.0017
19 13 1.0000 1.0000 1.0000 0.9999 0.9996 0.9969 0.9682 0.8371 0.6480 0.5261 0.3322 0.1631 0.0086
19 14 1.0000 1.0000 1.0000 1.0000 0.9999 0.9994 0.9904 0.9304 0.8120 0.7178 0.5346 0.3267 0.0352
19 15 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9978 0.9770 0.9213 0.8668 0.7369 0.5449 0.1150
19 16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9996 0.9945 0.9760 0.9538 0.8887 0.7631 0.2946
19 17 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9992 0.9953 0.9896 0.9690 0.9171 0.5797
19 18 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9995 0.9989 0.9958 0.9856 0.8649
19 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
Table A.9 Cumulative Binomial Distribution…

𝒏 𝒙 𝒑 = 𝟎. 𝟏 𝒑 = 𝟎. 𝟐 𝒑 = 𝟎. 𝟐𝟓 𝒑 = 𝟎. 𝟑 𝒑 = 𝟏⁄𝟑 𝒑 = 𝟎. 𝟒 𝒑 = 𝟎. 𝟓 𝒑 = 𝟎. 𝟔 𝒑 = 𝟐⁄𝟑 𝒑 = 𝟎. 𝟕 𝒑 = 𝟎. 𝟕𝟓 𝒑 = 𝟎. 𝟖 𝒑 = 𝟎. 𝟗

20 0 0.1216 0.0115 0.0032 0.0008 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
20 1 0.3917 0.0692 0.0243 0.0076 0.0033 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
20 2 0.6769 0.2061 0.0913 0.0355 0.0176 0.0036 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
20 3 0.8670 0.4114 0.2252 0.1071 0.0605 0.0160 0.0013 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
20 4 0.9568 0.6296 0.4148 0.2375 0.1516 0.0510 0.0059 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000
20 5 0.9887 0.8042 0.6172 0.4164 0.2973 0.1256 0.0207 0.0016 0.0002 0.0000 0.0000 0.0000 0.0000
20 6 0.9976 0.9133 0.7858 0.6080 0.4795 0.2500 0.0577 0.0065 0.0009 0.0003 0.0000 0.0000 0.0000
20 7 0.9996 0.9679 0.8982 0.7723 0.6616 0.4159 0.1316 0.0210 0.0037 0.0013 0.0002 0.0000 0.0000
20 8 0.9999 0.9900 0.9591 0.8867 0.8095 0.5956 0.2517 0.0565 0.0130 0.0051 0.0009 0.0001 0.0000
20 9 1.0000 0.9974 0.9861 0.9520 0.9082 0.7553 0.4119 0.1275 0.0376 0.0171 0.0039 0.0006 0.0000
20 10 1.0000 0.9994 0.9961 0.9829 0.9624 0.8725 0.5881 0.2447 0.0918 0.0480 0.0139 0.0026 0.0000
20 11 1.0000 0.9999 0.9991 0.9949 0.9870 0.9435 0.7483 0.4044 0.1905 0.1133 0.0409 0.0100 0.0001
20 12 1.0000 1.0000 0.9998 0.9987 0.9963 0.9790 0.8684 0.5841 0.3384 0.2277 0.1018 0.0321 0.0004
20 13 1.0000 1.0000 1.0000 0.9997 0.9991 0.9935 0.9423 0.7500 0.5205 0.3920 0.2142 0.0867 0.0024
20 14 1.0000 1.0000 1.0000 1.0000 0.9998 0.9984 0.9793 0.8744 0.7027 0.5836 0.3828 0.1958 0.0113
20 15 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9941 0.9490 0.8484 0.7625 0.5852 0.3704 0.0432
20 16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9981 0.9840 0.9395 0.8929 0.7748 0.5886 0.1330
20 17 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9964 0.9824 0.9645 0.9087 0.7939 0.3231
20 18 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9967 0.9924 0.9757 0.9308 0.6083
20 19 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9991 0.9992 0.9968 0.9885 0.8784
20 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
Table A.10 Cumulative Binomial Distribution…

𝒏 𝒙 𝒑 = 𝟎. 𝟏 𝒑 = 𝟎. 𝟐 𝒑 = 𝟎. 𝟐𝟓 𝒑 = 𝟎. 𝟑 𝒑 = 𝟏⁄𝟑 𝒑 = 𝟎. 𝟒 𝒑 = 𝟎. 𝟓 𝒑 = 𝟎. 𝟔 𝒑 = 𝟐⁄𝟑 𝒑 = 𝟎. 𝟕 𝒑 = 𝟎. 𝟕𝟓 𝒑 = 𝟎. 𝟖 𝒑 = 𝟎. 𝟗

25 0 0.0718 0.0038 0.0008 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
25 1 0.2712 0.0274 0.0070 0.0016 0.0005 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
25 2 0.5371 0.0982 0.0321 0.0090 0.0035 0.0004 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
25 3 0.7636 0.2340 0.0962 0.0332 0.0149 0.0024 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
25 4 0.9020 0.4207 0.2137 0.0905 0.0462 0.0095 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
25 5 0.9666 0.6167 0.3783 0.1935 0.1120 0.0294 0.0020 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000
25 6 0.9905 0.7800 0.5611 0.3407 0.2216 0.0736 0.0073 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000
25 7 0.9977 0.8909 0.7265 0.5118 0.3704 0.1536 0.0216 0.0012 0.0001 0.0000 0.0000 0.0000 0.0000
25 8 0.9995 0.9532 0.8506 0.6769 0.5377 0.2735 0.0539 0.0043 0.0004 0.0001 0.0000 0.0000 0.0000
25 9 0.9999 0.9827 0.9287 0.8106 0.6957 0.4246 0.1148 0.0132 0.0016 0.0015 0.0000 0.0000 0.0000
25 10 1.0000 0.9944 0.9703 0.9022 0.8211 0.5858 0.2122 0.0344 0.0056 0.0018 0.0001 0.0000 0.0000
25 11 1.0000 0.9985 0.9893 0.9558 0.9083 0.7323 0.3450 0.0778 0.0164 0.0060 0.0009 0.0001 0.0000
25 12 1.0000 0.9996 0.9966 0.9825 0.9585 0.8462 0.5000 0.1538 0.0415 0.0175 0.0034 0.0004 0.0000
25 13 1.0000 0.9999 0.9991 0.9940 0.9836 0.9222 0.6550 0.2677 0.0917 0.0442 0.0107 0.0015 0.0000
25 14 1.0000 1.0000 0.9998 0.9982 0.9944 0.9656 0.7878 0.4142 0.1779 0.0978 0.0297 0.0056 0.0000
25 15 1.0000 1.0000 1.0000 0.9995 0.9984 0.9868 0.8852 0.5754 0.3043 0.1894 0.0713 0.0173 0.0001
25 16 1.0000 1.0000 1.0000 0.9999 0.9996 0.9957 0.9461 0.7265 0.4623 0.3131 0.1494 0.0468 0.0005
25 17 1.0000 1.0000 1.0000 1.0000 0.9999 0.9988 0.9784 0.8464 0.6296 0.4881 0.1735 0.1091 0.0023
25 18 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9917 0.9264 0.7784 0.6593 0.4389 0.1200 0.0095
25 19 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9980 0.9706 0.8880 0.8065 0.6217 0.3833 0.0334
25 20 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9905 0.9538 0.9095 0.7863 0.5793 0.0980
25 21 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9976 0.9851 0.9668 0.9038 0.7660 0.2364
25 22 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9996 0.9965 0.9910 0.9679 0.9018 0.4619
25 23 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9995 0.9984 0.9930 0.9716 0.7288
25 24 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9991 0.9961 0.9282
25 25 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
Table B.1 Cumulative Poisson Distribution


𝒙
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0 0.9048 0.8187 0.7408 0.6703 0.6065 0.5488 0.4966 0.4493 0.4066 0.3679
1 0.9953 0.9825 0.9631 0.9384 0.9098 0.8781 0.8442 0.8088 0.7725 0.7358
2 0.9998 0.9989 0.9964 0.9921 0.9856 0.9769 0.9659 0.9526 0.9371 0.9197
3 1.0000 0.9999 0.9997 0.9992 0.9982 0.9966 0.9942 0.9909 0.9865 0.9810
4 1.0000 1.0000 1.0000 0.9999 0.9998 0.9996 0.9992 0.9986 0.9977 0.9963
5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9994
6 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


𝒙
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
0 0.3329 0.3012 0.2725 0.2466 0.2231 0.2019 0.1827 0.1653 0.1496 0.1353
1 0.6990 0.6626 0.6268 0.5918 0.5578 0.5249 0.4932 0.4628 0.4337 0.4060
2 0.9004 0.8795 0.8571 0.8335 0.8088 0.7834 0.7572 0.7306 0.7037 0.6767
3 0.9743 0.9662 0.9569 0.9463 0.9344 0.9212 0.9068 0.8913 0.8747 0.8571
4 0.9946 0.9923 0.9893 0.9857 0.9814 0.9763 0.9704 0.9636 0.9559 0.9473
5 0.9990 0.9985 0.9978 0.9968 0.9955 0.9940 0.9920 0.9896 0.9868 0.9834
6 0.9999 0.9997 0.9996 0.9994 0.9991 0.9987 0.9981 0.9974 0.9966 0.9955
7 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994 0.9992 0.9989
8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9998
9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000


𝒙
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
0 0.1225 0.1108 0.1003 0.0907 0.0821 0.0743 0.0672 0.0608 0.0550 0.0498
1 0.3796 0.3546 0.3309 0.3084 0.2873 0.2674 0.2487 0.2311 0.2146 0.1991
2 0.6496 0.6227 0.5960 0.5697 0.5438 0.5184 0.4936 0.4695 0.4460 0.4232
3 0.8386 0.8194 0.7993 0.7787 0.7576 0.7360 0.7141 0.6919 0.6696 0.6472
4 0.9379 0.9275 0.9162 0.9041 0.8912 0.8774 0.8629 0.8477 0.8318 0.8153
5 0.9796 0.9751 0.9700 0.9643 0.9580 0.9510 0.9433 0.9349 0.9258 0.9161
6 0.9941 0.9925 0.9906 0.9884 0.9858 0.9828 0.9794 0.9756 0.9713 0.9665
7 0.9985 0.9980 0.9974 0.9967 0.9958 0.9947 0.9934 0.9919 0.9901 0.9881
8 0.9997 0.9995 0.9994 0.9991 0.9989 0.9985 0.9981 0.9976 0.9969 0.9962
9 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9995 0.9993 0.9991 0.9989
10 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997
11 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
Table B.2 Cumulative Poisson Distribution…


𝒙
3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0
0 0.0450 0.0408 0.0369 0.0334 0.0302 0.0273 0.0247 0.0224 0.0202 0.0183
1 0.1847 0.1712 0.1586 0.1468 0.1359 0.1257 0.1162 0.1074 0.0992 0.0916
2 0.4012 0.3799 0.3594 0.3397 0.3208 0.3027 0.2854 0.2689 0.2531 0.2381
3 0.6248 0.6025 0.5803 0.5584 0.5366 0.5152 0.4942 0.4735 0.4532 0.4335
4 0.7982 0.7806 0.7626 0.7442 0.7254 0.7064 0.6872 0.6678 0.6484 0.6288
5 0.9057 0.8946 0.8829 0.8705 0.8576 0.8441 0.8301 0.8156 0.8006 0.7851
6 0.9612 0.9554 0.9490 0.9421 0.9347 0.9267 0.9182 0.9091 0.8995 0.8893
7 0.9858 0.9832 0.9802 0.9769 0.9733 0.9692 0.9648 0.9599 0.9546 0.9489
8 0.9953 0.9943 0.9931 0.9917 0.9901 0.9883 0.9863 0.9840 0.9815 0.9786
9 0.9986 0.9982 0.9978 0.9973 0.9967 0.9960 0.9952 0.9942 0.9931 0.9919
10 0.9996 0.9995 0.9994 0.9992 0.9990 0.9987 0.9984 0.9981 0.9977 0.9972
11 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9995 0.9994 0.9993 0.9991
12 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997
13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999
14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000


𝒙
4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0
0 0.0166 0.0150 0.0136 0.0123 0.0111 0.0101 0.0091 0.0082 0.0074 0.0067
1 0.0845 0.0780 0.0719 0.0663 0.0611 0.0563 0.0518 0.0477 0.0439 0.0404
2 0.2238 0.2102 0.1974 0.1851 0.1736 0.1626 0.1523 0.1425 0.1333 0.1247
3 0.4142 0.3954 0.3772 0.3594 0.3423 0.3257 0.3097 0.2942 0.2793 0.2650
4 0.6093 0.5898 0.5704 0.5512 0.5321 0.5132 0.4946 0.4763 0.4582 0.4405
5 0.7693 0.7531 0.7367 0.7199 0.7029 0.6858 0.6684 0.6510 0.6335 0.6160
6 0.8786 0.8675 0.8558 0.8436 0.8311 0.8180 0.8046 0.7908 0.7767 0.7622
7 0.9427 0.9361 0.9290 0.9214 0.9134 0.9049 0.8960 0.8867 0.8769 0.8666
8 0.9755 0.9721 0.9683 0.9642 0.9597 0.9549 0.9497 0.9442 0.9382 0.9319
9 0.9905 0.9889 0.9871 0.9851 0.9829 0.9805 0.9778 0.9749 0.9717 0.9682
10 0.9966 0.9959 0.9952 0.9943 0.9933 0.9922 0.9910 0.9896 0.9880 0.9863
11 0.9989 0.9986 0.9983 0.9980 0.9976 0.9971 0.9966 0.9960 0.9953 0.9945
12 0.9997 0.9996 0.9995 0.9993 0.9992 0.9990 0.9988 0.9986 0.9983 0.9980
13 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 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 1.0000 1.0000 1.0000 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
Table C.1 Standard Normal Distribution

Selected percentiles:
Area: 0.100 0.050 0.025 0.020 0.010 0.005
𝒛 −1.282 −1.645 −1.960 −2.054 −2.326 −2.576

𝒛 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
−3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002
−3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003
−3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005
−3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007
−3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010
−2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014
−2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019
−2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026
−2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036
−2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048
−2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064
−2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084
−2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110
−2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143
−2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183
−1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233
−1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294
−1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367
−1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455
−1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559
−1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681
−1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823
−1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985
−1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170
−1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379
−0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611
−0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867
−0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148
−0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451
−0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776
−0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121
−0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483
−0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859
−0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247
−0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641
For 𝑧 values less than −3.49, use 0.0001.
 Table C.2 Standard Normal Distribution…

Selected percentiles:
Area: 0.900 0.950 0.975 0.980 0.990 0.995
𝒛 1.282 1.645 1.960 2.054 2.326 2.576

𝒛 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517
0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879
0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852
0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133
0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633
1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767
2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817
2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857
2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890
2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964
2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974
2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990
3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993
3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995
3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997
3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998

For 𝑧 values greater than 3.49, use 0.9999.

Table D t-distribution

Cumulative Percentage Points for the Student’s t-distribution

𝜶𝜶
𝒅𝒅𝒅𝒅
0.900 0.950 0.975 0.990 0.995
1 3.078 6.314 12.706 31.821 63.656
2 1.886 2.920 4.303 6.965 9.925
3 1.638 2.353 3.182 4.541 5.841
4 1.533 2.132 2.776 3.747 4.604
5 1.476 2.015 2.571 3.365 4.032
6 1.440 1.943 2.447 3.143 3.707
7 1.415 1.895 2.365 2.998 3.499
8 1.397 1.860 2.306 2.896 3.355
9 1.383 1.833 2.262 2.821 3.250
10 1.372 1.812 2.228 2.764 3.169
11 1.363 1.796 2.201 2.718 3.106
12 1.356 1.782 2.179 2.681 3.055
13 1.350 1.771 2.160 2.650 3.012
14 1.345 1.761 2.145 2.624 2.977
15 1.341 1.753 2.131 2.602 2.947
16 1.337 1.746 2.120 2.583 2.921
17 1.333 1.740 2.110 2.567 2.898
18 1.330 1.734 2.101 2.552 2.878
19 1.328 1.729 2.093 2.539 2.861
20 1.325 1.725 2.086 2.528 2.845
21 1.323 1.721 2.080 2.518 2.831
22 1.321 1.717 2.074 2.508 2.819
23 1.319 1.714 2.069 2.500 2.807
24 1.318 1.711 2.064 2.492 2.797
25 1.316 1.708 2.060 2.485 2.787
26 1.315 1.706 2.056 2.479 2.779
27 1.314 1.703 2.052 2.473 2.771
28 1.313 1.701 2.048 2.467 2.763
29 1.311 1.699 2.045 2.462 2.756
30 1.310 1.697 2.042 2.457 2.750
31 1.309 1.696 2.040 2.453 2.744
32 1.309 1.694 2.037 2.449 2.738
33 1.308 1.692 2.035 2.445 2.733
34 1.307 1.691 2.032 2.441 2.728
35 1.306 1.690 2.030 2.438 2.724
36 1.306 1.688 2.028 2.434 2.719
37 1.305 1.687 2.026 2.431 2.715
38 1.304 1.686 2.024 2.429 2.712
39 1.304 1.685 2.023 2.426 2.708
40 1.303 1.684 2.021 2.423 2.704
∞ 1.282 1.645 1.96 2.327 2.576
Table E 𝝌𝝌𝟐𝟐-distribution

𝑃𝑃�𝜒𝜒 2 < 𝜒𝜒𝜈𝜈;𝛼𝛼

2
� = 𝛼𝛼 0.025

0.025

𝜶𝜶 𝟏𝟏 − 𝜶𝜶 𝟎𝟎. 𝟗𝟗𝟗𝟗

𝝌𝝌𝟐𝟐𝝂𝝂;𝜶𝜶 𝝌𝝌𝟐𝟐𝟒𝟒;𝟎𝟎.𝟎𝟎𝟎𝟎𝟎𝟎 𝝌𝝌𝟐𝟐𝟒𝟒;𝟎𝟎.𝟗𝟗𝟗𝟗𝟓𝟓

= 𝟎𝟎. 𝟒𝟒𝟒𝟒𝟒𝟒 = 𝟏𝟏𝟏𝟏. 𝟏𝟏𝟏𝟏𝟏𝟏

Area to the left of the Critical Value of 𝝌𝝌𝟐𝟐

𝒅𝒅𝒅𝒅 0.005 0.01 0.025 0.05 0.10 0.90 0.95 0.975 0.99 0.995
1 0.000 0.000 0.001 0.004 0.016 2.706 3.841 5.024 6.635 7.879
2 0.010 0.020 0.051 0.103 0.211 4.605 5.991 7.378 9.210 10.597
3 0.072 0.115 0.216 0.352 0.584 6.251 7.815 9.348 11.345 12.838
4 0.207 0.297 0.484 0.711 1.064 7.779 9.488 11.143 13.277 14.860
5 0.412 0.554 0.831 1.145 1.610 9.236 11.070 12.833 15.086 16.750
6 0.676 0.872 1.237 1.635 2.204 10.645 12.592 14.449 16.812 18.548
7 0.989 1.239 1.690 2.167 2.833 12.017 14.067 16.013 18.475 20.278
8 1.344 1.646 2.180 2.733 3.490 13.362 15.507 17.535 20.090 21.955
9 1.735 2.088 2.700 3.325 4.168 14.684 16.919 19.023 21.666 23.589
10 2.156 2.558 3.247 3.940 4.865 15.987 18.307 20.483 23.209 25.188
11 2.603 3.053 3.816 4.575 5.578 17.275 19.675 21.920 24.725 26.757
12 3.074 3.571 4.404 5.226 6.304 18.549 21.026 23.337 26.217 28.300
13 3.565 4.107 5.009 5.892 7.042 19.812 22.362 24.736 27.688 29.819
14 4.075 4.660 5.629 6.571 7.790 21.064 23.685 26.119 29.141 31.319
15 4.601 5.229 6.262 7.261 8.547 22.307 24.996 27.488 30.578 32.801
16 5.142 5.812 6.908 7.962 9.312 23.542 26.296 28.845 32.000 34.267
17 5.697 6.408 7.564 8.672 10.085 24.769 27.587 30.191 33.409 35.718
18 6.265 7.015 8.231 9.390 10.865 25.989 28.869 31.526 34.805 37.156
19 6.844 7.633 8.907 10.117 11.651 27.204 30.144 32.852 36.191 38.582
20 7.434 8.260 9.591 10.851 12.443 28.412 31.410 34.170 37.566 39.997
21 8.034 8.897 10.283 11.591 13.240 29.615 32.671 35.479 38.932 41.401
22 8.643 9.542 10.982 12.338 14.041 30.813 33.924 36.781 40.289 42.796
23 9.260 10.196 11.689 13.091 14.848 32.007 35.172 38.076 41.638 44.181
24 9.886 10.856 12.401 13.848 15.659 33.196 36.415 39.364 42.980 45.559
25 10.520 11.524 13.120 14.611 16.473 34.382 37.652 40.646 44.314 46.928
26 11.160 12.198 13.844 15.379 17.292 35.563 38.885 41.923 45.642 48.290
27 11.808 12.879 14.573 16.151 18.114 36.741 40.113 43.195 46.963 49.645
28 12.461 13.565 15.308 16.928 18.939 37.916 41.337 44.461 48.278 50.993
29 13.121 14.256 16.047 17.708 19.768 39.087 42.557 45.722 49.588 52.336
30 13.787 14.953 16.791 18.493 20.599 40.256 43.773 46.979 50.892 53.672
40 20.707 22.164 24.433 26.509 29.051 51.805 55.758 59.342 63.691 66.766
50 27.991 29.707 32.357 34.764 37.689 63.167 67.505 71.420 76.154 79.490
60 35.534 37.485 40.482 43.188 46.459 74.397 79.082 83.298 88.379 91.952
70 43.275 45.442 48.758 51.739 55.329 85.527 90.531 95.023 100.425 104.215
80 51.172 53.540 57.153 60.391 64.278 96.578 101.879 106.629 112.329 116.321
90 59.196 61.754 65.647 69.126 73.291 107.565 113.145 118.136 124.116 128.299
100 67.328 70.065 74.222 77.929 82.358 118.498 124.342 129.561 135.807 140.169
Table F.1 F-Distribution

𝑃𝑃�𝐹𝐹 < 𝐹𝐹5;6; 0,95 � = 0.95

0.05

0.95

𝐹𝐹5; 6; 0,95
= 4.39

Percentage points for the F-distribution (𝑑𝑑𝑑𝑑2 between 1 and 7)

𝒅𝒅𝒅𝒅𝟏𝟏
𝒅𝒅𝒅𝒅𝟐𝟐 𝜶𝜶 1 2 3 4 5 6 7 8 9
0.90 39.86 49.50 53.59 55.83 57.24 58.20 58.91 59.44 59.86
0.95 161.45 199.50 215.71 224.58 230.16 233.99 236.77 238.88 240.54
1 0.975 647.79 799.50 864.16 899.58 921.85 937.11 948.22 956.66 963.28
0.99 4052.2 4999.5 5403.4 5624.6 5763.6 5859.0 5928.4 5981.1 6022.5

0.90 8.53 9.00 9.16 9.24 9.29 9.33 9.35 9.37 9.38
0.95 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38
2 0.975 38.51 39.00 39.17 39.25 39.30 39.33 39.36 39.37 39.39
0.99 98.50 99.00 99.17 99.25 99.30 99.33 99.36 99.37 99.39

0.90 5.54 5.46 5.39 5.34 5.31 5.28 5.27 5.25 5.24
0.95 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81
3 0.975 17.44 16.04 15.44 15.10 14.88 14.73 14.62 14.54 14.47
0.99 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.35

0.90 4.54 4.32 4.19 4.11 4.05 4.01 3.98 3.95 3.94
0.95 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00
4 0.975 12.22 10.65 9.98 9.60 9.36 9.20 9.07 8.98 8.90
0.99 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.66

0.90 4.06 3.78 3.62 3.52 3.45 3.40 3.37 3.34 3.32
0.95 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77
5 0.975 10.01 8.43 7.76 7.39 7.15 6.98 6.85 6.76 6.68
0.99 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16

0.90 3.78 3.46 3.29 3.18 3.11 3.05 3.01 2.98 2.96
0.95 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10
6 0.975 8.81 7.26 6.60 6.23 5.99 5.82 5.70 5.60 5.52
0.99 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.10 7.98

0.90 3.59 3.26 3.07 2.96 2.88 2.83 2.78 2.75 2.72
0.95 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68
7 0.975 8.07 6.54 5.89 5.52 5.29 5.12 4.99 4.90 4.82
0.99 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72
 Table F.2 F-Distribution…

0.05

0.95

𝐹𝐹5; 6; 0,05 = 1�𝐹𝐹 = 1�4.95 = 0.20

6; 5; 0,95

Percentage points for the F-distribution (𝑑𝑑𝑑𝑑2 between 1 and 7)

𝒅𝒅𝒅𝒅𝟏𝟏
𝒅𝒅𝒅𝒅𝟐𝟐 𝜶𝜶 10 12 15 20 25 30 40 60 120 ∞
0.90 60.19 60.71 61.22 61.74 62.05 62.26 62.53 62.79 63.06 63.33
0.95 241.88 243.91 245.95 248.01 249.26 250.10 251.14 252.20 253.25 254.30
1 0.975 968.63 976.71 984.87 993.10 998.08 1001.40 1005.60 1009.80 1014.00 1018.00
0.99 6055.8 6106.3 6157.3 6208.7 6239.8 6260.6 6286.8 6313.0 6339.4 63666

0.90 9.39 9.41 9.42 9.44 9.45 9.46 9.47 9.47 9.48 9.49
0.95 19.40 19.41 19.43 19.45 19.46 19.46 19.47 19.48 19.49 19.50
2 0.975 39.40 39.41 39.43 39.45 39.46 39.46 39.47 39.48 39.49 39.50
0.99 99.40 99.42 99.43 99.45 99.46 99.47 99.47 99.48 99.49 99.50

0.90 5.23 5.22 5.20 5.18 5.17 5.17 5.16 5.15 5.14 5.13
0.95 8.79 8.74 8.70 8.66 8.63 8.62 8.59 8.57 8.55 8.53
3 0.975 14.42 14.34 14.25 14.17 14.12 14.08 14.04 13.99 13.95 13.90
0.99 27.23 27.05 26.87 26.69 26.58 26.50 26.41 26.32 26.22 26.13

0.90 3.92 3.90 3.87 3.84 3.83 3.82 3.80 3.79 3.78 3.76
0.95 5.96 5.91 5.86 5.80 5.77 5.75 5.72 5.69 5.66 5.63
4 0.975 8.84 8.75 8.66 8.56 8.50 8.46 8.41 8.36 8.31 8.26
0.99 14.55 14.37 14.20 14.02 13.91 13.84 13.75 13.65 13.56 13.46

0.90 3.30 3.27 3.24 3.21 3.19 3.17 3.16 3.14 3.12 3.10
0.95 4.74 4.68 4.62 4.56 4.52 4.50 4.46 4.43 4.40 4.36
5 0.975 6.62 6.52 6.43 6.33 6.27 6.23 6.18 6.12 6.07 6.02
0.99 10.05 9.89 9.72 9.55 9.45 9.38 9.29 9.20 9.11 9.02

0.90 2.94 2.90 2.87 2.84 2.81 2.80 2.78 2.76 2.74 2.72
0.95 4.06 4.00 3.94 3.87 3.83 3.81 3.77 3.74 3.70 3.67
6 0.975 5.46 5.37 5.27 5.17 5.11 5.07 5.01 4.96 4.90 4.85
0.99 7.87 7.72 7.56 7.40 7.30 7.23 7.14 7.06 6.97 6.88

0.90 2.70 2.67 2.63 2.59 2.57 2.56 2.54 2.51 2.49 2.47
0.95 3.64 3.57 3.51 3.44 3.40 3.38 3.34 3.30 3.27 3.23
7 0.975 4.76 4.67 4.57 4.47 4.40 4.36 4.31 4.25 4.20 4.14
0.99 6.62 6.47 6.31 6.16 6.06 5.99 5.91 5.82 5.74 5.65
 Table F.3 F-Distribution…
Percentage points for the F-distribution (𝑑𝑑𝑑𝑑2 between 8 and 16)
𝒅𝒅𝒅𝒅𝟏𝟏
𝒅𝒅𝒅𝒅𝟐𝟐 𝜶𝜶
1 2 3 4 5 6 7 8 9
0.90 3.46 3.11 2.92 2.81 2.73 2.67 2.62 2.59 2.56
0.95 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39
8 0.975 7.57 6.06 5.42 5.05 4.82 4.65 4.53 4.43 4.36
0.99 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91

0.90 3.36 3.01 2.81 2.69 2.61 2.55 2.51 2.47 2.44
0.95 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18
9 0.975 7.21 5.71 5.08 4.72 4.48 4.32 4.20 4.10 4.03
0.99 10.56 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35

0.90 3.29 2.92 2.73 2.61 2.52 2.46 2.41 2.38 2.35
0.95 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02
10 0.975 6.94 5.46 4.83 4.47 4.24 4.07 3.95 3.85 3.78
0.99 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94

0.90 3.23 2.86 2.66 2.54 2.45 2.39 2.34 2.30 2.27
0.95 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90
11 0.975 6.72 5.26 4.63 4.28 4.04 3.88 3.76 3.66 3.59
0.99 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63

0.90 3.18 2.81 2.61 2.48 2.39 2.33 2.28 2.24 2.21
0.95 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80
12 0.975 6.55 5.10 4.47 4.12 3.89 3.73 3.61 3.51 3.44
0.99 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39

0.90 3.14 2.76 2.56 2.43 2.35 2.28 2.23 2.20 2.16
0.95 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71
13 0.975 6.41 4.97 4.35 4.00 3.77 3.60 3.48 3.39 3.31
0.99 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19

0.90 3.10 2.73 2.52 2.39 2.31 2.24 2.19 2.15 2.12
0.95 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65
14 0.975 6.30 4.86 4.24 3.89 3.66 3.50 3.38 3.29 3.21
0.99 8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 4.03

0.90 3.07 2.70 2.49 2.36 2.27 2.21 2.16 2.12 2.09
0.95 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59
15 0.975 6.20 4.77 4.15 3.80 3.58 3.41 3.29 3.20 3.12
0.99 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89

0.90 3.05 2.67 2.46 2.33 2.24 2.18 2.13 2.09 2.06
0.95 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54
16 0.975 6.12 4.69 4.08 3.73 3.50 3.34 3.22 3.12 3.05
0.99 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78
 Table F.4 F-Distribution…
Percentage points for the F-distribution (𝑑𝑑𝑑𝑑2 between 8 and 16)
𝒅𝒅𝒅𝒅𝟏𝟏
𝒅𝒅𝒅𝒅𝟐𝟐 𝜶𝜶 10 12 15 20 25 30 40 60 120 ∞
0.90 2.54 2.50 2.46 2.42 2.40 2.38 2.36 2.34 2.32 2.29
0.95 3.35 3.28 3.22 3.15 3.11 3.08 3.04 3.01 2.97 2.93
8 0.975 4.30 4.20 4.10 4.00 3.94 3.89 3.84 3.78 3.73 3.67
0.99 5.81 5.67 5.52 5.36 5.26 5.20 5.12 5.03 4.95 4.86

0.90 2.42 2.38 2.34 2.30 2.27 2.25 2.23 2.21 2.18 2.16
0.95 3.14 3.07 3.01 2.94 2.89 2.86 2.83 2.79 2.75 2.71
9 0.975 3.96 3.87 3.77 3.67 3.60 3.56 3.51 3.45 3.39 3.33
0.99 5.26 5.11 4.96 4.81 4.71 4.65 4.57 4.48 4.40 4.31

0.90 2.32 2.28 2.24 2.20 2.17 2.16 2.13 2.11 2.08 2.06
0.95 2.98 2.91 2.85 2.77 2.73 2.70 2.66 2.62 2.58 2.54
10 0.975 3.72 3.62 3.52 3.42 3.35 3.31 3.26 3.20 3.14 3.08
0.99 4.85 4.71 4.56 4.41 4.31 4.25 4.17 4.08 4.00 3.91

0.90 2.25 2.21 2.17 2.12 2.10 2.08 2.05 2.03 2.00 1.97
0.95 2.85 2.79 2.72 2.65 2.60 2.57 2.53 2.49 2.45 2.40
11 0.975 3.53 3.43 3.33 3.23 3.16 3.12 3.06 3.00 2.94 2.88
0.99 4.54 4.40 4.25 4.10 4.01 3.94 3.86 3.78 3.69 3.60

0.90 2.19 2.15 2.10 2.06 2.03 2.01 1.99 1.96 1.93 1.90
0.95 2.75 2.69 2.62 2.54 2.50 2.47 2.43 2.38 2.34 2.30
12 0.975 3.37 3.28 3.18 3.07 3.01 2.96 2.91 2.85 2.79 2.72
0.99 4.30 4.16 4.01 3.86 3.76 3.70 3.62 3.54 3.45 3.36

0.90 2.14 2.10 2.05 2.01 1.98 1.96 1.93 1.90 1.88 1.85
0.95 2.67 2.60 2.53 2.46 2.41 2.38 2.34 2.30 2.25 2.21
13 0.975 3.25 3.15 3.05 2.95 2.88 2.84 2.78 2.72 2.66 2.60
0.99 4.10 3.96 3.82 3.66 3.57 3.51 3.43 3.34 3.25 3.17

0.90 2.10 2.05 2.01 1.96 1.93 1.91 1.89 1.86 1.83 1.80
0.95 2.60 2.53 2.46 2.39 2.34 2.31 2.27 2.22 2.18 2.13
14 0.975 3.15 3.05 2.95 2.84 2.78 2.73 2.67 2.61 2.55 2.49
0.99 3.94 3.80 3.66 3.51 3.41 3.35 3.27 3.18 3.09 3.00

0.90 2.06 2.02 1.97 1.92 1.89 1.87 1.85 1.82 1.79 1.76
0.95 2.54 2.48 2.40 2.33 2.28 2.25 2.20 2.16 2.11 2.07
15 0.975 3.06 2.96 2.86 2.76 2.69 2.64 2.59 2.52 2.46 2.40
0.99 3.80 3.67 3.52 3.37 3.28 3.21 3.13 3.05 2.96 2.87

0.90 2.03 1.99 1.94 1.89 1.86 1.84 1.81 1.78 1.75 1.72
0.95 2.49 2.42 2.35 2.28 2.23 2.19 2.15 2.11 2.06 2.01
16 0.975 2.99 2.89 2.79 2.68 2.61 2.57 2.51 2.45 2.38 2.32
0.99 3.69 3.55 3.41 3.26 3.16 3.10 3.02 2.93 2.84 2.75
 Table F.5 F-Distribution…
Percentage points for the F-distribution (𝑑𝑑𝑑𝑑2 between 17 and 25)
𝒅𝒅𝒅𝒅𝟏𝟏
𝒅𝒅𝒅𝒅𝟐𝟐 𝜶𝜶
1 2 3 4 5 6 7 8 9
0.90 3.03 2.64 2.44 2.31 2.22 2.15 2.10 2.06 2.03
0.95 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49
17 0.975 6.04 4.62 4.01 3.66 3.44 3.28 3.16 3.06 2.98
0.99 8.40 6.11 5.19 4.67 4.34 4.10 3.93 3.79 3.68

0.90 3.01 2.62 2.42 2.29 2.20 2.13 2.08 2.04 2.00
0.95 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46
18 0.975 5.98 4.56 3.95 3.61 3.38 3.22 3.10 3.01 2.93
0.99 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60

0.90 2.99 2.61 2.40 2.27 2.18 2.11 2.06 2.02 1.98
0.95 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42
19 0.975 5.92 4.51 3.90 3.56 3.33 3.17 3.05 2.96 2.88
0.99 8.18 5.93 5.01 4.50 4.17 3.94 3.77 3.63 3.52

0.90 2.97 2.59 2.38 2.25 2.16 2.09 2.04 2.00 1.96
0.95 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39
20 0.975 5.87 4.46 3.86 3.51 3.29 3.13 3.01 2.91 2.84
0.99 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46

0.90 2.96 2.57 2.36 2.23 2.14 2.08 2.02 1.98 1.95
0.95 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37
21 0.975 5.83 4.42 3.82 3.48 3.25 3.09 2.97 2.87 2.80
0.99 8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51 3.40

0.90 2.95 2.56 2.35 2.22 2.13 2.06 2.01 1.97 1.93
0.95 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34
22 0.975 5.79 4.38 3.78 3.44 3.22 3.05 2.93 2.84 2.76
0.99 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35

0.90 2.94 2.55 2.34 2.21 2.11 2.05 1.99 1.95 1.92
0.95 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32
23 0.975 5.75 4.35 3.75 3.41 3.18 3.02 2.90 2.81 2.73
0.99 7.88 5.66 4.76 4.26 3.94 3.71 3.54 3.41 3.30

0.90 2.93 2.54 2.33 2.19 2.10 2.04 1.98 1.94 1.91
0.95 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30
24 0.975 5.72 4.32 3.72 3.38 3.15 2.99 2.87 2.78 2.70
0.99 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26

0.90 2.92 2.53 2.32 2.18 2.09 2.02 1.97 1.93 1.89
0.95 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28
25 0.975 5.69 4.29 3.69 3.35 3.13 2.97 2.85 2.75 2.68
0.99 7.77 5.57 4.68 4.18 3.85 3.63 3.46 3.32 3.22
 Table F.6 F-Distribution…
Percentage points for the F-distribution (𝑑𝑑𝑑𝑑2 between 17 and 25)
𝒅𝒅𝒅𝒅𝟏𝟏
𝒅𝒅𝒅𝒅𝟐𝟐 𝜶𝜶 10 12 15 20 25 30 40 60 120 ∞
0.90 2.00 1.96 1.91 1.86 1.83 1.81 1.78 1.75 1.72 1.69
0.95 2.45 2.38 2.31 2.23 2.18 2.15 2.10 2.06 2.01 1.97
17 0.975 2.92 2.82 2.72 2.62 2.55 2.50 2.44 2.38 2.32 2.26
0.99 3.59 3.46 3.31 3.16 3.07 3.00 2.92 2.83 2.75 2.66

0.90 1.98 1.93 1.89 1.84 1.80 1.78 1.75 1.72 1.69 1.66
0.95 2.41 2.34 2.27 2.19 2.14 2.11 2.06 2.02 1.97 1.96
18 0.975 2.87 2.77 2.67 2.56 2.49 2.44 2.38 2.32 2.26 2.25
0.99 3.51 3.37 3.23 3.08 2.98 2.92 2.84 2.75 2.66 2.65

0.90 1.96 1.91 1.86 1.81 1.78 1.76 1.73 1.70 1.67 1.63
0.95 2.38 2.31 2.23 2.16 2.11 2.07 2.03 1.98 1.93 1.88
19 0.975 2.82 2.72 2.62 2.51 2.44 2.39 2.33 2.27 2.20 2.13
0.99 3.43 3.30 3.15 3.00 2.91 2.84 2.76 2.67 2.58 2.49

0.90 1.94 1.89 1.84 1.79 1.76 1.74 1.71 1.68 1.64 1.61
0.95 2.35 2.28 2.20 2.12 2.07 2.04 1.99 1.95 1.90 1.84
20 0.975 2.77 2.68 2.57 2.46 2.40 2.35 2.29 2.22 2.16 2.09
0.99 3.37 3.23 3.09 2.94 2.84 2.78 2.69 2.61 2.52 2.42

0.90 1.92 1.87 1.83 1.78 1.74 1.72 1.69 1.66 1.62 1.59
0.95 2.32 2.25 2.18 2.10 2.05 2.01 1.96 1.92 1.87 1.81
21 0.975 2.73 2.64 2.53 2.42 2.36 2.31 2.25 2.18 2.11 2.04
0.99 3.31 3.17 3.03 2.88 2.79 2.72 2.64 2.55 2.46 2.36

0.90 1.90 1.86 1.81 1.76 1.73 1.70 1.67 1.64 1.60 1.57
0.95 2.30 2.23 2.15 2.07 2.02 1.98 1.94 1.89 1.84 1.78
22 0.975 2.70 2.60 2.50 2.39 2.32 2.27 2.21 2.14 2.08 2.00
0.99 3.26 3.12 2.98 2.83 2.73 2.67 2.58 2.50 2.40 2.31

0.90 1.89 1.84 1.80 1.74 1.71 1.69 1.66 1.62 1.59 1.55
0.95 2.27 2.20 2.13 2.05 2.00 1.96 1.91 1.86 1.81 1.76
23 0.975 2.67 2.57 2.47 2.36 2.29 2.24 2.18 2.11 2.04 1.97
0.99 3.21 3.07 2.93 2.78 2.69 2.62 2.54 2.45 2.35 2.26

0.90 1.88 1.83 1.78 1.73 1.70 1.67 1.64 1.61 1.57 1.53
0.95 2.25 2.18 2.11 2.03 1.97 1.94 1.89 1.84 1.79 1.73
24 0.975 2.64 2.54 2.44 2.33 2.26 2.21 2.15 2.08 2.01 1.94
0.99 3.17 3.03 2.89 2.74 2.64 2.58 2.49 2.40 2.31 2.21

0.90 1.87 1.82 1.77 1.72 1.68 1.66 1.63 1.59 1.56 1.52
0.95 2.24 2.16 2.09 2.01 1.96 1.92 1.87 1.82 1.77 1.71
25 0.975 2.61 2.51 2.41 2.30 2.23 2.18 2.12 2.05 1.98 1.91
0.99 3.13 2.99 2.85 2.70 2.60 2.54 2.45 2.36 2.27 2.17
 Table F.7 F-Distribution…
Percentage points for the F-distribution (𝑑𝑑𝑑𝑑2 between 26 and ∞)
𝒅𝒅𝒅𝒅𝟏𝟏
𝒅𝒅𝒅𝒅𝟐𝟐 𝜶𝜶
1 2 3 4 5 6 7 8 9
0.90 2.91 2.52 2.31 2.17 2.08 2.01 1.96 1.92 1.88
0.95 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27
26 0.975 5.66 4.27 3.67 3.33 3.10 2.94 2.82 2.73 2.65
0.99 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18

0.90 2.90 2.51 2.30 2.17 2.07 2.00 1.95 1.91 1.87
0.95 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25
27 0.975 5.63 4.24 3.65 3.31 3.08 2.92 2.80 2.71 2.63
0.99 7.68 5.49 4.60 4.11 3.78 3.56 3.39 3.26 3.15

0.90 2.89 2.50 2.29 2.16 2.06 2.00 1.94 1.90 1.87
0.95 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24
28 0.975 5.61 4.22 3.63 3.29 3.06 2.90 2.78 2.69 2.61
0.99 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12

0.90 2.89 2.50 2.28 2.15 2.06 1.99 1.93 1.89 1.86
0.95 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28 2.22
29 0.975 5.59 4.20 3.61 3.27 3.04 2.88 2.76 2.67 2.59
0.99 7.60 5.42 4.54 4.04 3.73 3.50 3.33 3.20 3.09

0.90 2.88 2.49 2.28 2.14 2.05 1.98 1.93 1.88 1.85
0.95 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21
30 0.975 5.57 4.18 3.59 3.25 3.03 2.87 2.75 2.65 2.57
0.99 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07

0.90 2.84 2.44 2.23 2.09 2.00 1.93 1.87 1.83 1.79
0.95 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12
40 0.975 5.42 4.05 3.46 3.13 2.90 2.74 2.62 2.53 2.45
0.99 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89

0.90 2.79 2.39 2.18 2.04 1.95 1.87 1.82 1.77 1.74
0.95 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04
60 0.975 5.29 3.93 3.34 3.01 2.79 2.63 2.51 2.41 2.33
0.99 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72

0.90 2.76 2.36 2.14 2.00 1.91 1.83 1.78 1.73 1.69
0.95 3.94 3.09 2.70 2.46 2.31 2.19 2.10 2.03 1.97
100 0.975 5.18 3.83 3.25 2.92 2.70 2.54 2.42 2.32 2.24
0.99 6.90 4.82 3.98 3.51 3.21 2.99 2.82 2.69 2.59

0.90 2.71 2.30 2.08 1.94 1.85 1.77 1.72 1.67 1.63
0.95 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.88
∞ 0.975 5.02 3.69 3.12 2.79 2.57 2.41 2.29 2.19 2.11
0.99 6.63 4.61 3.78 3.32 3.02 2.80 2.64 2.51 2.41
 Table F.8 F-Distribution…
Percentage points for the F-distribution (𝑑𝑑𝑑𝑑2 between 26 and ∞)
𝒅𝒅𝒅𝒅𝟏𝟏
𝒅𝒅𝒅𝒅𝟐𝟐 𝜶𝜶 10 12 15 20 25 30 40 60 120 ∞
0.90 1.86 1.81 1.76 1.71 1.67 1.65 1.61 1.58 1.54 1.50
0.95 2.22 2.15 2.07 1.99 1.94 1.90 1.85 1.80 1.75 1.69
26 0.975 2.59 2.49 2.39 2.28 2.21 2.16 2.09 2.03 1.95 1.88
0.99 3.09 2.96 2.81 2.66 2.57 2.50 2.42 2.33 2.23 2.13

0.90 1.85 1.80 1.75 1.70 1.66 1.64 1.60 1.57 1.53 1.49
0.95 2.20 2.13 2.06 1.97 1.92 1.88 1.84 1.79 1.73 1.67
27 0.975 2.57 2.47 2.36 2.25 2.18 2.13 2.07 2.00 1.93 1.85
0.99 3.06 2.93 2.78 2.63 2.54 2.47 2.38 2.29 2.20 2.10

0.90 1.84 1.79 1.74 1.69 1.65 1.63 1.59 1.56 1.52 1.48
0.95 2.19 2.12 2.04 1.96 1.91 1.87 1.82 1.77 1.71 1.65
28 0.975 2.55 2.45 2.34 2.23 2.16 2.11 2.05 1.98 1.91 1.83
0.99 3.03 2.90 2.75 2.60 2.51 2.44 2.35 2.26 2.17 2.06

0.90 1.83 1.78 1.73 1.68 1.64 1.62 1.58 1.55 1.51 1.47
0.95 2.18 2.10 2.03 1.94 1.89 1.85 1.81 1.75 1.70 1.64
29 0.975 2.53 2.43 2.32 2.21 2.14 2.09 2.03 1.96 1.89 1.81
0.99 3.00 2.87 2.73 2.57 2.48 2.41 2.33 2.23 2.14 2.03

0.90 1.82 1.77 1.72 1.67 1.63 1.61 1.57 1.54 1.50 1.46
0.95 2.16 2.09 2.01 1.93 1.88 1.84 1.79 1.74 1.68 1.62
30 0.975 2.51 2.41 2.31 2.20 2.12 2.07 2.01 1.94 1.87 1.79
0.99 2.98 2.84 2.70 2.55 2.45 2.39 2.30 2.21 2.11 2.01

0.90 1.76 1.71 1.66 1.61 1.57 1.54 1.51 1.47 1.42 1.38
0.95 2.08 2.00 1.92 1.84 1.78 1.74 1.69 1.64 1.58 1.52
40 0.975 2.39 2.29 2.18 2.07 1.99 1.94 1.88 1.80 1.72 1.65
0.99 2.80 2.66 2.52 2.37 2.27 2.20 2.11 2.02 1.92 1.82

0.90 1.71 1.66 1.60 1.54 1.50 1.48 1.44 1.40 1.35 1.29
0.95 1.99 1.92 1.84 1.75 1.69 1.65 1.59 1.53 1.47 1.39
60 0.975 2.27 2.17 2.06 1.94 1.87 1.82 1.74 1.67 1.58 1.48
0.99 2.63 2.50 2.35 2.20 2.10 2.03 1.94 1.84 1.73 1.60

0.90 1.66 1.61 1.56 1.49 1.45 1.42 1.38 1.34 1.28 1.21
0.95 1.93 1.85 1.77 1.68 1.62 1.57 1.52 1.45 1.38 1.29
100 0.975 2.18 2.08 1.97 1.85 1.77 1.71 1.64 1.56 1.46 1.36
0.99 2.50 2.37 2.22 2.07 1.97 1.89 1.80 1.69 1.57 1.45

0.90 1.60 1.55 1.49 1.42 1.38 1.34 1.30 1.24 1.17 1.08
0.95 1.83 1.75 1.67 1.57 1.52 1.46 1.39 1.32 1.22 1.11
∞ 0.975 2.05 1.94 1.83 1.71 1.64 1.57 1.48 1.49 1.27 1.13
0.99 2.32 2.18 2.04 1.88 1.79 1.70 1.59 1.47 1.32 1.16