Suppose the heights of 18-year-old men are approximatelynormally distributed, with mean 66 inches and standard deviation 6inches.
(a) What is the probability that an 18-year-old man selected atrandom is between 65 and 67 inches tall? (Round your answer to fourdecimal places.)
(b) If a random sample of eighteen 18-year-old men is selected,what is the probability that the mean height x is between 65 and 67inches? (Round your answer to four decimal places.)
(c) Compare your answers to parts (a) and (b). Is theprobability in part (b) much higher? Why would you expect this?
The probability in part (b) is much higher because the standarddeviation is larger for the x distribution.
The probability in part (b) is much higher because the mean issmaller for the x distribution. The probability in part (b) is muchlower because the standard deviation is smaller for the xdistribution.
The probability in part (b) is much higher because the standarddeviation is smaller for the x distribution.
The probability in part (b) is much higher because the mean islarger for the x distribution.
