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Every weekend, a local station gets to do a nighttime radio show on XM station 27. During the show, the show's host plays 40 rock-androll songs during each 4hour 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-androll 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-androll songs. {b} If the program manager schedules 30 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 rockandroll songs exceeds the available airtime