In trying to determine the sphere of influence of a sports centre a random sample of 100 visitors was taken. This indicated a mean travel distance (d) of 10 miles with a standard deviation of 3 miles:...

In trying to determine the sphere of influence of a sports centre a random sample of 100 visitors was taken. This indicated a mean travel distance (d) of 10 miles with a standard deviation of 3 miles: (a) What are the 90% confidence limits for the population mean travel distance (D), and (b) What sample size would be required to ensure that the confidence interval for D was 0.5 miles at the 95% level?