Question: Vital Statistics: Heights of men

The heights of 18-year-old men are approximately normally distributed, with mean 68 inches and standard deviation 3 inches.

a.) What is the probability that an 18-year-old man selected at random is between 67 and 69 inches tall?

b.) If a random sample of nine 18-year-old men is selected, what is the probability

that the mean height x is between 67 and 69 inches?

c.) Compare your answers for part (a) and (b). Is the probability in part (b) much

higher? Why would you expect this?