To help shape her promotional strategy, the general manager of a regional airport wants to know how far passengers travel to use the airport. The mean and standard deviation of the distances travelled by a random sample of 61 passengers were 24.1 miles and 5.8 miles respectively.
(a) Find a 90% confidence interval for the mean distance travelled by passengers.
(b) If the population standard deviation were later found to be 6.3 miles, what size sample would be needed in order to estimate the mean distance travelled by passengers for the error to be one mile with a 90% level of confidence?