6.68 A bank web operation officer is monitoring online credit card transactions and determines that the transaction duration follows a normal distribution with a mean of 20 seconds and a standard deviation of 7 seconds.

A random sample of 16 such transaction durations is taken.

a. What is the probability that the sample mean credit card transaction duration is more than 22 seconds?

b. What is the probability that the sample mean credit card transaction duration is between 17 and 22 seconds?

c. The probability is 0.25 that the sample mean credit card transaction duration is less than what value?

d. The probability is 0.025 that the sample standard deviation of credit card transaction duration is more than what value?

e. If a sample of 25 of these credit cards’ transaction durations was taken, state whether the probability of a sample mean credit card transaction duration of more than 22 seconds would be smaller than, larger than, or the same as the correct answer to part (a).

Sketch a graph to illustrate your reasoning.