Suppose the heights of 18-year-old men are approximatelynormally distributed, with mean 67 inches and standarddeviation 6 inches.
(a) What is the probability that an 18-year-old man selected atrandom is between 66 and 68 inches tall? (Round your answer to fourdecimal places.)
(b) If a random sample of thirteen 18-year-old men is selected,what is the probability that the mean height x is between66 and 68 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 issmaller for the x distribution.The probability in part (b)is much lower because the standard deviation is smaller for thex distribution.    The probability inpart (b) is much higher because the mean is larger for thex distribution.The probability in part (b) is much higherbecause the standard deviation is smaller for the xdistribution.The probability in part (b) is much higher because thestandard deviation is larger for the x distribution.
