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 (based on information from Statistical Abstract of the United States, 1 12th Edition).

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 \[\bar{X}\] is between 67 and 69 inches tall?

c.) Compare your answers for parts (c) and (b). Is the probability in part (b) much higher? Why would you expect this?