The amount of time the university professors devote to their jobs per week is normally dis- tributed with a mean of 52 hours and a standard deviation of 8 hours.

Question

(a) What is the probability that a professor works for more than 56 hours per week?
(b) Find the probability that the mean amount of work per week for four randomly selected professors is more than 56 hours.
(c) Find the probability that the mean amount of work per week for 36 randomly selected professors is more than 56 hours.
(d) If the devoted time to job is not normally distributed, which, if any, of the questions can you answer? Explain.

Answer 1

a) Z = (score-mean)/SD

Look in the back of your statistics textbook for a table called something like “area under normal distribution” to find the proportion/probability related to the Z score.

b, c) Z = (score-mean)/SEm

SEm = SD/√n

Use same table.

I'll leave the explanation up to you.