A corporation has 272 accounts receivable in a particular category. A random sample of 50 of them was taken. The sample mean was $492.36, and the sample standard deviation was $149.92.

a. Find a 99% confidence interval for the population mean value of these accounts receivable.

b. Find a 95% confidence interval for the total value of these accounts receivable.

c. Without doing the calculations, state whether a 90% confidence interval for the population total would be wider or narrower than the interval found in part b.