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=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.

Step-by-step explanation:

Given that 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.

Sample proportion =

the proportion of all UNC students that are foreign students is 0.061.

i.e. Population proportion= 0.061

Mean for 50 size sample = sample proportion = 0.08

Std deviation of sample proportion =

Hence for the ampling distribution of the sample proportion for a sample of size 50, mean =0.08 and std dev = 0.0338

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