Suppose the heights of 18-year-old men are approximatelynormally distributed, with mean 68 inches and standarddeviation 2 inches.
(a) What is the probability that an 18-year-old man selected atrandom is between 67 and 69 inches tall? (Round your answer to fourdecimal places.)
(b) If a random sample of twenty-nine 18-year-old men is selected,what is the probability that the mean height x is between67 and 69 inches? (Round your answer to four decimal places.)
(c) Compare your answers to parts (a) and (b). Is the probabilityin part (b) much higher? Why would you expect this?
The probability in part (b) is much higher because the mean islarger for the x distribution.The probability in part (b)is much higher because the standard deviation is larger for thex distribution. The probability inpart (b) is much lower because the standard deviation is smallerfor the x distribution.The probability in part (b) is muchhigher because the mean is smaller for the xdistribution.The probability in part (b) is much higher because thestandard deviation is smaller for the x distribution.
