Background data: Norman Bates has just inherited $40,000. Consultants identified guest showers as the most significant use of water. They calculated that the lengths of guest showers at the Bates Motel are normally distributed with a mean of 10 minutes and a standard deviation of 3 minutes.

Question: Suppose on a particular Tuesday night two years ago there were eight guests checked into the hotel and that each guest took exactly one shower. What is the probability that the average length of the eight showers was more than 12 minutes?

Please use excel for the answer. Please show the excel formulas and calculations used to get the answer.