Movie rentals. To compete with Netflix, the owner of a movie rental shop decided to try sending DVDs through the mail. In order to determine how many copies of newly released titles he should purchase, he carefully observed turnaround times. Since nearly all of his customers were in his local community, he tested delivery times by sending DVDs to his friends. He found the mean delivery time was 1.3 days, with a standard deviation of 0.5 days. He also noted that the times were the same whether going to the customer or coming back to the shop.

a)    Find the mean and standard deviation of the round-trip delivery times for a DVD (mailed to the customer and then mailed back to the shop).

b)    The shop owner tries to process a DVD that is returned to him and get it back in the mail in one day, but circum- stances sometimes prevent it. His mean turnaround time is 1.1 days, with a standard deviation of 0.3 days. Find the mean and standard deviation of the turnaround times com- bined with the round-trip times in part a.