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.

$X~\_\_\_\_\_(\_\_\_\_\_,\_\_\_\_\_)$

Short answer

The response variable has a Hypergeometric distribution having coefficients $r,b\&n$, whereby $r$represents the size of the first group (of concern), $b$denotes the size of the second group, and $n$reflects the sample size. It's referred to as$X~H(r,b,n)i.e.,X~H(16,7,9)$

Step-by-step solution

Concept used

Hypergeometric distribution: A randomised experiment is considered hypergeometric if it comprises of two groups and a sample is drawn from the combined group without replacement. The group with concern is one of the two groups. The 'number of hits within the sample' is the event of interest here. The hypergeometric distribution is supplemented by a hypergeometric experimentation.

Given

There really are two different groups, one of which is the business significant group, which is the group of interest. The variable $X$will be written as follows:

$X$is the number of local majors chosen inside the sample.

In addition, the size of its first group (the group of concern) is $r$, the size of the second group is $b$, and the sample group is $n$.

Explanation

Because $X$has a hypergeometric distribution, it may be written as: $X~H(r,b,n)$

So, $\mathrm{X}~\mathrm{H}(16,7,9)$