6.66 A study determines that the height of Taiwanese men aged 65 or more is normally distributed with an average of 163.8 centimeters and standard deviation of 6.2 centimeters. A random sample of 20 Taiwanese elderly men is taken.

a. Find the probability that the sample mean height is higher than 165.

b. Find the probability that the sample mean height is between 160 and 165.

c. The probability is 0.01 that the sample mean height is higher than what value?

d. The probability is 0.01 that the sample mean height is lower than what value?

e. The probability is 0.05 that the sample standard deviation of the heights is higher than what value?

f. The probability is 0.05 that the sample standard deviation of the heights is lower than what value?

g. If a sample of 60 Taiwanese men’s heights had been taken, would the probability of a sample mean height more than 165 be smaller than, larger than, or the same as the answer in part (a)? It is not necessary to do the detailed calculations here. Explain how the graph would change based on your reasoning.