A computer store has 50 printers of which 40 are laser printers and 10 are ink jet printers. If a group of 10 printers is chosen at random from the store, find the mean and variance of the number of ink jet
Printers.
A) Mean = 2, Variance = 0.2
B) Mean = 2, Variance = 3
C) Mean = 1, Variance = 0.2
D) Mean = 2, Variance = 1.6

Question

Quizplus · Accepted Answer

We can solve this problem using the hypergeometric distribution, where X is the number of ink jet printers in a sample of 10 printers.

The mean of X is given by:

E(X) = n * (M / N)

where n is the sample size (10), M is the number of ink jet printers in the store (10), and N is the total number of printers in the store (50).

Plugging in the values, we get:

E(X) = 10 * (10 / 50) = 2

The variance of X is given by:

Var(X) = n * (M / N) * ((N - M) / N) * ((N - n) / (N - 1))

Plugging in the values, we get:

Var(X) = 10 * (10 / 50) * (40 / 50) * (40 / 49) = 1.6

Therefore, the best choice is D, with a mean of 2 and variance of 1.6.

A Computer Store Has 50 Printers of Which 40 Are