According to home-water-works.org, the average shower in the United States lasts 8.2 minutes. Assume the standard deviation of shower times is 2 minutes and the distribution of shower times is right-skewed.

Which of the following questions can be answered using the Central Limit Theorem for sample means as needed? If the question can be answered, do so. If the question cannot be answered, explain why the Central Limit Theorem cannot be applied.

a. Find the probability that a randomly selected shower lasts more than 9 minutes.

b. If five showers are randomly selected, find the probability that the mean length of the sample is more than 9 minutes.

c. If 50 showers are randomly selected, find the probability that the mean length of the sample is more than 9 minutes.