The amount of time the university professors devote to their jobs per week is normally distributed with a mean of 52 hours and a standard deviation of 6 hours.

a) What is the probability that a professor works for more than 60 hours per week?

b) Determine the probability that the mean amount of work per week for three randomly selected professors is more than 60 hours.

c) Determine the probability that if three professors are randomly selected, all three work for more than 60 hours per week.