Question

This is a two part question A small liberal arts college in the northeast has 350 freshman. 90 of the freshman are education majors. Supposed 70 freshman are randomly selected without replacement 1. find the expected number of education majors in the sample round your answer to two decimal places if necessary 2. find the standard deviation of the number of education majors in the sample

Answer 1

Step-by-step explanation:

Given:

Total number of freshmen = 350

Number of education majors = 90

Number of randomly selected freshmen without replacement = 70

To find:

The expected number of education majors in the sample

Let's go ahead and determine what fraction of freshmen are education majors;

`(90)/(350)=(9)/(35)`

If 70 freshmen are randomly selected, we can determine the expected number of education majors in the sample as seen below;

`\begin{gathered} Expected\text{ }Number\text{ of Education majors}=(9)/(35)*70 \\ =9*2 \\ =18 \end{gathered}`

Therefore, the expected number of education majors in the sample is 18

We'll go ahead and determine the standard deviation of the number of education majors in the sample using the below formula;