The TSA PreCheck program is intended to be a way to shorten airline security lines for “trusted travelers.”

Suppose 13,000 people living in a major southern city paid an annual $80 fee to participate in the program.

They spent an average of 200 seconds in security lines. For comparison purposes, suppose a sample was obtained of the time it took the other passengers to pass through security a TSA check station. The file titled PASSTIME contains these data. Assume the distribution of time required to pass through security for those flyers in the PreCheck program is normally distributed.

a. Calculate the sample mean and the sample standard deviation for this sample of passenger times.

b. Assume that the distribution of the time required to pass through security is normally distributed. Use the sample data to construct a 95% confidence interval for the average time required to pass through security.

c. What is the margin of error for the confidence interval constructed in part b?