Question 2: [15 marks]

Part a) (7 marks) A sample of = 25 observations is drawn from a normal population with = 100 and = 20. Find the following.

i) ( < 90)

ii) (90 < < 105)

Part b) (8 marks) The amount of time the university professors devote to their jobs per week is normally distributed with a mean of 50 hours and a standard deviation of 10 hours.

i) What is the probability that a professor works for more than 80 hours per week?

ii) Find the probability that the mean amount of work per week for two randomly selected professors is more than 60 hours?