A local radio station plays 40 rock-and-roll songs during each 4-hour show. The program director at the station needs to know th
e 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 new 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.
