Solved Problems in Statistics Hypergeometric 2014
Solved Problems in Statistics Hypergeometric 2014
Solved Problems in Statistics Hypergeometric 2014
Prepared by:
Charlie A. Marquez, PIE
September 12, 2014
HYPERGEOMETRIC DISTRIBUTION
The probability distribution of the hypergeometric random variable X, the
number of successes in a random sample of size n selected from N items of
which k are labeled success and N-k labeled failure, is
h(x;N,n,k) = (kCx)(N-kCn-x) / NCn , x = 0,1,2,…,n.
B. 0.3011 D. NOTA
B. 0.2015 D. NOTA
B. ½ D. NOTA
5. A team of 3rd party inspectors from the EU Community suspects that some
manufacturers from China are in violation of child labor. 20 firms are under
suspicion but all cannot be visited. Suppose that 3 of the companies are in
violation, what is the probability that visit and inspection of 5 firms finds no
violations?
A. 0.1937 C.0.3991
B. 0.1316 D. NOTA
6. A third party auditor has an inspection system for batches of small items
purchased. A batch typically contains 15 items. In the inspection system, a
random sample of 5 is selected and all are tested. Suppose there are 2
faulty items in the batch of 15, what is the probability that inspection will
discover both faulty items?
A. 0.0952 C.0.0033
B. 0.4762 D. NOTA
7. A fishbowl contains 3 green balls, 2 blue balls, and 4 red balls. In a random
sample of 5 balls, find the probability that both blue balls and at least 1 red
ball are selected.
A. 0.0317 c. 0.2698
B. 0.1428 D. NOTA
B. 0.0606 D. NOTA
9. It is estimated that 4,000 of the new 10,000 students are not in favor of a
change in their uniforms. If 15 of the new students are selected at random
and asked their opinion, what is the probability that at most 7 favor the
new uniform?
A. 0.2131 C.0.2173
B. 0.7869 D. NOTA
B. 0.32 D. NOTA
11. What is the probability that a waitress will refuse to serve alcoholic
beverages to only two minors if she randomly checks the ID’s of 5 students
from among 9 students of which 4 are still minors?
A. 0.0794 C.0.0476
B. 0.4762 D. NOTA
12. From a lot of 10 ipods, 4 are selected at random and tested. If the lot
contains 3 defective ipods that will not work when tested, what is the
probability that all 4 will work?
A. 0.1666 C.0.6667
B. 0.0190 D. NOTA
B. 0.2315 D. NOTA
2. A nationwide survey of 17,000 call center agents revealed that almost 70%
disapprove the use of a certain type of headset. If 18 of these agents are
selected at random and asked their opinions , what is the probability that
more than 9 but less than 14 disapprove the use of this type of headset?
A. 0.6077 C.0.6257
B. 0.7758 D. NOTA
B. 0.6778 D. NOTA
B. 0.3106 D. NOTA
6. If 7 cards are dealt from an ordinary deck of 52 playing cards, what is the
probability that exactly 2 of them will be face cards?
A. 0.4496 C.0.8154
B. 0.3246 D. NOTA
B. 0.0129 D. NOTA
8. A team of 3rd party inspectors from the EU Community suspects that some
manufacturers from China are in violation of child labor. 20 firms are under
suspicion but all cannot be visited. Suppose that 3 of the companies are in
violation, what is the probability that visit and inspection of 5 firms finds no
violations?
A. 0.1316 C.0.0439
B. 0.3991 D. NOTA
9. A third party auditor has an inspection system for batches of small items
purchased. A batch typically contains 15 items. In the inspection system, a
random sample of 5 is selected and all are tested. Suppose there are 2
faulty items in the batch of 15, what is the probability that for a given
sample, there will be 1 faulty item?
A. 0.4762 C.0.3991
B. 0.1316 D. NOTA
B. 0.8906 D. NOTA