In planning for hot water requirements, the manager of the Luxurion Hotel finds that guests spend a mean of 11.4 min each day in the shower. Assume that the shower times are normally distributed with a standard deviation of 2.6 min.
a.Find the percentage of guests who shower more than 12 min.
b.The hotel has installed a system that can provide enough hot water provided that the mean shower time for 84 guests is less than 12 min. If the hotel currently has 84 guests, find the probability that there will not be enough hot water. Does the current system appear to be effective?