Suppose the heights of 18-year-old men are approximately normally distributed, with mean 68 inches and standard deviation 2 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 to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?