Question

The Office of Student Services at UNC would like to estimate the proportion of UNC's 34,000 students who are foreign students. In their random sample of 50 students, 4 are foreign students. Unknown to them, the proportion of all UNC students that are foreign students is 0.061. For each student, let x=1 if the student is foreign and let x=0 if the student is from the U.S. Find the mean and the standard deviation of the sampling distribution of the sample proportion for a sample of size 50.

Answer 1

Answer:

Mean is 3.05

Standard deviation is 1.69.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they are foreign, or they are not. This means that we can solve this problem using concepts of the binomial probability distribution.

Binomial probability distribution

The probability of x sucesses on n repeated trials, with p probability.

In this problem, we have a sample of 50 students, so $n = 50$. The proportion of all UNC students that are foreign students is 0.061, so $p = 0.061$.

The mean is given by the following formula:

$E(X) = np = 50*0.061 = 3.05$

The standard deviation is given by the following formula:

$\sigma = \sqrt{n*p*(1-p)} = \sqrt{50*0.061*(1-0.061))} = 1.69$