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.

1. What is the probability that an 18 year old man selected at random is between 67 and 69 inches tall?
2. 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?
3. Compare your answers for parts (a) and (b). Was the probability in part (b) much higher? Why would you expect this?

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