Problem 23BB

Hypergeometric Distribution A statistics class consists of 10 females and 30 males, and each day, 12 of the students are randomly selected without replacement. Because the sampling is from a small finite population without replacement, the hypergeometric distribution applies. Using the hypergeometric distribution, find the mean and standard deviation for the numbers of females that are selected on the different days.

Answer:

Step 1 of 1

Given, A statistics class consists of 10 females and 30 males, and each day, 12 of the students are randomly selected without replacement.

Using the hypergeometric distribution, we need to find the mean and standard deviation for the numbers of females that are selected on the different days.

Given, N = 40, n = 12, M = 10 females

Mean E(X) = = 3

Variance V(X) = [][]

= [][]

= [][]

= (0.7179)(3)(0.75)

= 1.6152

Standard deviation = = 1.2709