# Question: In this exercise we discuss the hypergeometric distribution in more

In this exercise, we discuss the hypergeometric distribution in more detail. When sampling is done without replacement from a finite population, the hypergeometric distribution is the exact probability distribution for the number of members sampled that have a specified attribute. The hypergeometric probability formula is where X denotes the number of members sampled that have the specified attribute, N is the population size, n is the sample size, and p is the population proportion.

To illustrate, suppose that a customer purchases 4 fuses from a shipment of 250, of which 94% are not defective. Let a success correspond to a fuse that is not defective.

a. Determine N, n, and p.

b. Use the hypergeometric probability formula to find the probability distribution of the number of nondefective fuses the customer gets.

Key Fact 5.6 shows that a hypergeometric distribution can be approximated by a binomial distribution, provided the sample size does not exceed 5% of the population size. In particular, you can use the binomial probability formula

with n = 4 and p = 0.94, to approximate the probability distribution of the number of nondefective fuses that the customer gets.

c. Obtain the binomial distribution with parameters n = 4 and p = 0.94.

d. Compare the hypergeometric distribution that you obtained in part (b) with the binomial distribution that you obtained in part (c).

To illustrate, suppose that a customer purchases 4 fuses from a shipment of 250, of which 94% are not defective. Let a success correspond to a fuse that is not defective.

a. Determine N, n, and p.

b. Use the hypergeometric probability formula to find the probability distribution of the number of nondefective fuses the customer gets.

Key Fact 5.6 shows that a hypergeometric distribution can be approximated by a binomial distribution, provided the sample size does not exceed 5% of the population size. In particular, you can use the binomial probability formula

with n = 4 and p = 0.94, to approximate the probability distribution of the number of nondefective fuses that the customer gets.

c. Obtain the binomial distribution with parameters n = 4 and p = 0.94.

d. Compare the hypergeometric distribution that you obtained in part (b) with the binomial distribution that you obtained in part (c).

**View Solution:**## Answer to relevant Questions

In this exercise, we discuss the geometric distribution, the probability distribution for the number of trials until the first success in Bernoulli trials. The geometric probability formula is P(X = x) = p(1 − p)x−1, ...Concerning the equal-likelihood model of probability, a. What is it? b. How is the probability of an event found? Refer to Exercise 5.26. a. In 4000 human gestation periods, roughly how many will exceed 9 months? b. In 500 horse races, roughly how many times will the favorite finish in the money? c. In 389 traffic fatalities, roughly ...Construct a Venn diagram representing each event. a. (not E) b. (A or B) c. (A & B) d. (A & B & C) e. (A or B or C) f. ((not A) & B) In a report titled Behavioral Risk Factor Surveillance System Summary Prevalence Report, the Centers for Disease Control and Prevention discusses the prevalence of diabetes in the United States. The following frequency ...Post your question