A population of fish has an unknown average length . Assume that the lengths of the fish are normally distributed. Suppose a sample of size n = 25 bears is taken, and their average length X = 43 inches is calculated.

(a) Assume that the population standard deviation = 8 inches is known. Give a 90% confidence interval for the population mean.

(b) Assume that the population standard deviation is unknown, but that the sample standard deviation s = 7 inches is known. Give a 95% confidence interval for the population mean.