The amount of time the university professors devote to their jobs per week has a Normal distribution with an average of 52 hours and a standard deviation of 6 hours.

a) Identify the subjects of interest. [1]

b) Provide a description of the variable of interest and identify the type of the variable. [1]

c) Identify the statistic of interest and the notation. [1]

d) If three professors are randomly selected, what is the sampling distribution of the statistic defined in part (c)? [3]

e) If three professors are randomly selected, what is the probability that the sample average amount of time they work is more than 60 hours per week? [2]