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Probability based on normal distribution.

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, 112th 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 is between 67 and 69 inches?

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

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