.

A random survey of enrollment at 2020community colleges across the United States yielded the following figures:

21,8722 2,221; 9,414; 7,681;3,200;17,500;9,200; 7,380; 18,314; 6,557; 13,713; 17,768;7,493; 2,771; 2,861; 1,263; 7,285; 28,165; 5,080; 11,735

(a) Assume the underlying population is normal.

x=

ii.

sx=

iii.

n=

iv.

n1=

(b) Define the random variablesXandXin words

		Xis the number of students enrolled at a community college in the United States.Xis the mean number of students enrolled from the population of community colleges in the United States.
		Xis the number of students enrolled from a sampleof20community colleges in the United States.Xis the mean number of students enrolled in a community college in the United States.
		Xis the mean number of students enrolled from a sample of20community colleges in the United States.XXis the number of students enrolled at a community college in the United States.
		Xis the number of students enrolled at a community college in the United States.Xis the number of students enrolled from a sample of20community colleges in the United States.
		Xis the number of students enrolled at a community college in the United States.Xis the mean number of students enrolled from a sample of20community colleges in the United States.

(c) Which distribution should you use for this problem? Explain your choice.

		Xt19, sincethe sample size is smallis being used as an estimate forss.
		Xt20X, since the sample size is small andssis being used as an estimate for.
		XN(10,074,7,336), since the underlying population is normal.
		Xt19 since the sample size is small andssis being used as an estimate for.
		Xt20 sincethe sample size is smallis being used as an estimate forss.

(d) Construct a95%confidence interval for the population mean enrollment at community colleges in the United States.

Enter your answer in interval notation. Round your answer to the nearest integer. Do not round any intermediate calculations.

(e) What will happen to the error bound and confidence interval if77community colleges were surveyed? Why?

		The error bound and confidence interval will both decrease since decreasing the sample size increases variability in the sample.
		The error bound and confidence interval will both decrease since decreasing the sample size decreases variability in the sample.
		The error bound and confidence interval will both increase since decreasing the sample size decreases variability in the sample.
		The error bound and confidence interval will both increase since decreasing the sample size increases variability in the sample.