Question

A small liberal arts college in the Northeast has 350 freshmen. Ninety of the freshmen are education majors. Suppose seventy freshmen are randomly selected (withoutreplacement).Step 2 of 2: Find the standard deviation of the number of education majors in the sample. Round your answer to two decimal places, if necessary.AnswerKeypadKeyboard ShortcutsTables

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given details

For each freshmen, there are only two possible outcomes. Either it is an education majors holder, or it is not. Seventy freshmen are randomly selected (without replacement). This means that the hypergeometric distribution is used to solve this question.

STEP 2: Give the formula for calculating the standard deviation

Standard deviation of the hypergeometric distribution:

We have that:

N is the population size.

n is the sample size.

s is the number of successes in the sample.

The standard deviation is given by:

`\sigma=\sqrt{n((s)/(N))(1-(s)/(N))((N-n)/(N-1))}`

STEP 3: Write the given data

`\begin{gathered} N=350 \\ s=90 \\ n=70 \end{gathered}`

By substitution,

`\begin{gathered} \sigma=\sqrt{70((90)/(350))(1-(90)/(350))((350-70)/(350-1))} \\ \\ \sigma=√(10.7277937)=3.275331082 \\ \sigma=3.28 \end{gathered}`

Hence, the standard deviation is given approximately as 3.28