A study of college freshmen's study habits found that the time (in hours) that college freshmen use to study each week is approximately normally distributed with a mean of 7.2 hours and a standard deviation of 5.3 hours.

a.) What is the probability that a randomly chosen freshman studies more than twice the average number of hours? Include a sketch as part of your answer.

b.) Describe the sampling distribution of the mean x-bar of a sample of 55 randomly selected freshmen.

c.) What are the mean and standard deviation for the average number of hours x-bar spent studying by a SRS of 55 freshmen?

d.) What is the probability that the average number of hours spent studying of a SRS of 55 students is greater than 14.4 hours?

e.) Would your answers to parts a.) and d.) be affected if the distribution of numbers of hours freshmen study were distinctly non-normal? Explain briefly.