Reviewing his records, a grocery store manager finds that the amount of money spent shopping on Friday evenings is normally distributed with a standard deviation of $22. A random sample of 5 customers reveals the following amounts spent shopping on Friday night: $125, $72, $15, $88, and $96.

(a) Find a 95 % confidence interval for the mean amount of money spent shopping.

(b) Find a 90 % confidence interval for the mean amount of money spent shopping. Compare your answer to the confidence interval you computed in part (a). Which is larger?