When a certain machine breaks down, the repair time Y (in minutes) can be modeled by a gamma distribution with parameters = 1 and = 60. Of interest is the mean repair time (sample mean) of a sample of n=100 breakdowns. a) Find the expected value and the variance of the sample mean . b) What is the probability distribution that provides the best model of the sampling distribution of the sample mean Y? Why? c) What is the probability that the sample mean does not exceed 55 minutes? d) How large should the sample size n be if one wants the standard error not to exceed 2?