Suppose the heights of 18-year-old men are approximatelynormally distributed, with mean 68 inches and standarddeviation 4 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-six 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?
1The probability in part (b) is much higher because the standarddeviation is smaller for the x distribution. 2Theprobability in part (b) is much higher because the mean is largerfor the x distribution. 3The probability in part (b) ismuch lower because the standard deviation is smaller for thex distribution. 4The probability in part (b) is muchhigher because the standard deviation is larger for the xdistribution.5The probability in part (b) is much higher becausethe mean is smaller for the x distribution.
