A local radio station plays 40 rock-and-roll songs during each 4-hour show. The program director at the station
needs to know the total amount of airtime for the 40 songs so that time can also be programmed during the show
for news and advertisements. The distribution of the lengths of rock-and-roll songs, in minutes, is roughly
symmetric with a mean length of 3.9 minutes and a standard deviation of 1.1 minutes.
(a) Describe the sampling distribution of the sample mean song lengths for random samples of 40 rock-and-roll
songs
(b) If the program manager schedules 80 minutes of news and advertisements for the 4-hour (240-minute) show,
only 160 minutes are available for music. Approximately what is the probability that the total amount of
time needed to play 40 randomly selected rock-and-roll songs exceeds the available airtime?