Question

Use the following information to answer the next five exercises: Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are $16$business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested in the number of business majors in the sample.

Find the standard deviation.

Short answer

The standard deviation of the gaussian random $X$distributions is $\mathbf{1}\mathbf{.}\mathbf{1012}$.

Step-by-step solution

Formula used

The standard deviation of a hypergeometric distribution with parameters $r,b\&n$is given by:

$\sigma =\sqrt{\frac{rbn(r+b-n)}{(r+b{)}^2(r+b-1)}}$

Given

The values we are having:

$r=16,b=7$and$n=9$

Calculation

The standard deviation is calculated by multiplying $r=16,$$b=7$and$n=9$in the given formula:

localid="1649709225134" $$\begin{gathered} \sigma =\sqrt{\frac{16\times 7\times 9(16+7-9)}{(16+7{)}^2(16+7-1)}} \\ =1.1012 \end{gathered}$$