Question: An elevator has an occupancy warning of no more than 26 people and of total weight no more than 4000 pounds. For the population of users, suppose weights are approximately normal with mean 150 pounds and standard deviation 30 pounds.
a) What is the probability that the total weight of a random sample of 26 people from the population exceeds 400 pounds?
b) Suppose next that the people are carrying things and that the weight of these for an individual of weight X pounds, is approximately normal with mean 0.05X pounds and standard deviation 2 pounds. What is the probability that the total weight in the elevator now exceeds 4000 pounds?
c) The dimensions of the floor, of the elevator are 54 inches by 92inches. Suppose the amount of floor, space needed by users is normally distributed with mean µ square inches and standard deviation 0.1µ. Find µ. Find µ such that the probability 20 people can be accommodated is 0.99.