Reference no: EM132461596

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard deviation 2 inches.

(a) What is the probability that an 18-year-old man selected at random is between 70 and 72 inches tall?

(Round your answer to four decimal places.)

__________ ?

(b) If a random sample of nineteen 18-year-old men is selected, what is the probability that the mean height x is between 70 and 72 inches?

(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?

Choices:

• The probability in part (b) is much higher because the standard deviation is larger for the x distribution.
• The probability in part (b) is much higher because the mean is larger for the x distribution.    
• The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.
• The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.
• The probability in part (b) is much higher because the mean is smaller for the x distribution.