A sample of 27 students responded to a questionnaire regarding how many movies they viewed each year at the theater. Historically, the population mean and standard deviation have been believed to be 13 and 15.09.

(a) Could you use the Central Limit Theorem to calculate the probability that the mean number of movies was between 11 and 16? Explain your answer?

(b) Suppose a sample of 35 was obtained, rather than 27, and the mean and standard deviation remained the same. Calculate the probability the mean number of movies viewed by college students at the theater was between 11 and 16.?