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 manselected at random is between 71 and 73 inches tall? (Round youranswer to four decimal places.)
(b) If a random sample of thirty 18-year-old men isselected, what is the probability that the mean height xis between 71 and 73 inches? (Round your answer to four decimalplaces.)
(c) Compare your answers to parts (a) and (b). Is theprobability in part (b) much higher? Why would you expectthis?
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 lower because the standarddeviation is smaller 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 much higher because the standarddeviation is larger for the x distribution.
