A random sample of 50 12th-grade students was asked how long it took to get to school. The sample mean was 16.2 minutes, and the sample standard deviation was 12. minutes.

a. Find a 95% confidence interval for the population mean time it takes 12th-grade students to get to school.

b. Would a 90% confidence interval based on this sample data be wider or narrower than the 95% confidence interval? Explain. Check your answer by constructing a 90% confidence interval and comparing this width of the interval with the width of the 95% confidence interval you found in part a.