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, 112 ^th 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 (a) and (b). Is the probability in part (b) much higher? Why would you expect this?

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