In this exercise, we discuss the hypergeometric distribution in more detail. When sampling is done without replacement
Question:
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).
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...
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