Suppose the heights of 18-year-old men are approximatelynormally distributed, with mean 72 inches and standarddeviation 4 inches.
(a) What is the probability that an 18-year-old man selected atrandom is between 71 and 73 inches tall? (Round your answer to fourdecimal places.)
(b) If a random sample of twelve 18-year-old men is selected, whatis the probability that the mean height x is between 71and 73 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 standarddeviation is larger for the x distribution.
The probability in part (b) is much lower because the standarddeviation is smaller for the x distribution.
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
The probability in part (b) is much higher because the mean issmaller for the x distribution.
