A computer store has 75 printers of which 25 are laser printers and 50 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 = 3.3, Variance = 2.2
B) Mean = 6.7, Variance = 2.2
C) Mean = 3.3, Variance = 1.5
D) Mean = 6.7, Variance = 1.5

Question

Quizplus · Accepted Answer

The mean of the number of ink jet printers in a randomly chosen group of 10 from the store can be calculated using the formula for the expected value of a hypergeometric distribution, which is $n \times \frac{K}{N}$, where $n$ is the size of the group chosen (10 printers), $K$ is the total number of ink jet printers (50), and $N$ is the total number of printers (75). Thus, the mean is $10 \times \frac{50}{75} = 6.7$.The variance of the number of ink jet printers can be calculated using the formula for the variance of a hypergeometric distribution, which is $n \times \frac{K}{N} \times \left(1 - \frac{K}{N}\right) \times \frac{N-n}{N-1}$. Substituting the values, we get the variance as $10 \times \frac{50}{75} \times \left(1 - \frac{50}{75}\right) \times \frac{75-10}{75-1} = 2.2$.

A Computer Store Has 75 Printers of Which 25 Are