The Transportation Security Administration (TSA) has examined the possibility of a Registered Traveler program. This program is intended to be a way to shorten security lines for “trusted travelers.” In a study run at Orlando International Airport, 13,000 people paid an annual $80 fee to participate in the program. They spent an average of four seconds in security lines at Orlando according to Verified Identity Pass, the company that ran the program. For comparison purposes, a sample was obtained of the time it took the other passengers to pass through security at Orlando. The file titled PASSTIME contains these data. Assume the distribution of time required to pass through security at Orlando International Airport for those flyers in the Registered Traveler 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 time required to pass through security at Orlando International Airport 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 b?