According to home-water-works.org, the average shower in the United States lasts 8.2 minutes. Assume this is correct, and assume the standard deviation of 2 minutes.

a. Do you expect the shape of the distribution of shower lengths to be Normal, right skewed, or left-skewed? Explain.

b. Suppose that we survey a random sample of 100 people to find the length of their last shower. We calculate the mean length from the sample and record the value. We repeat this 500 times. What will be the shape of the distribution of these sample means?

c. Refer to part b. What will be the mean and the standard deviation of the distribution of these sample means?