Suppose the heights of 18-year-old men are approximatelynormally distributed, with mean 65 inches and standard deviation 6 inches.

(a) What is the probability that an 18-year-old man selected at random is between64and66inches tall? (Round your answer to four decimal places.)

(b) If a random sample ofseven 18-year-old men is selected, what is the probability that the mean heightxis between64 and66inches? (Round your answer to four decimal places.)

(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?

The probability in part (b) is much higher because the standard deviation is smaller for thexdistribution.

The probability in part (b) is much higher because the mean is larger for thexdistribution.

The probability in part (b) is much higher because the mean is smaller for thexdistribution.

The probability in part (b) is much higher because the standard deviation is larger for thexdistribution.

The probability in part (b) is much lower because the standard deviation is smaller for thexdistribution.