Jonathan conducted a study of the time his students spent studying per week. He found they have a distribution that is left-skewed with a mean of 7.8 hours and a standard deviation of 2.4 hours using a random sample of 45 students.

a) What is the sampling distribution of the mean number of hours these 45 students spend studying per week? (i.e. What is the sampling distribution of x ?)

b) Find the probability that the mean time spent studying per week is between 8 and 9 hours.