Question: Sports and Leisure. The Tonight Show with Johnny Carson lasted for 30 years and featured movie stars, comedians, animal acts, and Carnac the Magnificent. The first part of the show was reserved for Johnny's monologue. The mean length of a monologue was 12 minutes with standard deviation 45 seconds. Suppose 40 shows are selected at random and the length of each monologue is recorded.
a. Find the distribution of the total monologue time for the 40 shows, T.
b. Find P(T > 500).
c. Find P(470 ≤ T ≤ 490).
d. After his retirement, Johnny Carson's company started to sell DVDs of his monologues. Suppose one DVD holds 7.9 hours of recording. What is the probability that the company will be able to fit 40 randomly selected monologues onto one DVD?