Suppose the heights of 18-year-old men are

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 66 inchesand standard deviation 5 inches.(a) What is the probability that an 18-year-old man selected at random is between 65 and 67 inchestall? (Round your answer to four decimal places.)(b) If a random sample of thirty 18-year-old men is selected, what is the probability that the meanheight x is between 65 and 67 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 wouldyou expect this? (choose one answer)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 mean is smaller for the x distributionThe probability in part (b) is much higher because the standard deviation is smaller for the xdistribution.The probability in part (b) is much higher because the standard deviation is larger for the xdistribution.The probability in part (b) is much lower because the standard deviation is smaller for the xdistribution.

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