The heights of eighteen year old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches.

a. What is the probability that one randomly selected eighteen year old man will be less than 66 inches tall?

b. A random sample of 9 eighteen year old men is selected and the mean height of the sample, (x-bar) is calculated. Determine the mean and the standard deviation of the sampling distribution of (x-bar). Is this distribution normal? Explain how you can tell.

c. What is the probability that the mean of a sample of 9 eighteen year old men is less than 66 inches tall.

d. Compare the answers to (a) and (c) and explain why they are different.