Marcella takes a shower every morning when she gets up. Her time in the shower varies according to a Normal distribution with mean 4.5 minutes and standard deviation 0.9 minute.

a. Find the probability that Marcella’s shower lasts between 3 and 6 minutes on a randomly selected day.

b. If Marcella took a 7-minute shower, would it be classified as an outlier by the 1.5IQR rule? Justify your answer.

c. Suppose we choose 10 days at random and record the length of Marcella’s shower each day. What’s the probability that her shower time is 7 minutes or greater on at least 2 of the days?

d. Find the probability that the mean length of her shower times on these 10 days exceeds 5 minutes.