The Newport Varsity Club has 210 members. The weights of members have a distribution that is approximately normal with a mean of 163 lb and a standard deviation of 32 lb. The design for a new club building includes an elevator with a capacity limited to 12 passengers.

a. When considering the distribution of the mean weight of 12 passengers, should σ_x̅  be corrected by using the finite population correction factor? Explain.

b. If the elevator is designed to safely carry a load up to 2100 lb, what is the maximum safe mean weight when the elevator has 12 passengers?

c. If the elevator is filled with 12 randomly selected club members, what is the probability that the total load exceeds the safe limit of 2100 lb? Is this probability low enough?

d. What is the maximum number of passengers that should be allowed if we want a 0.999 probability that the elevator will not be overloaded when it is filled with randomly selected club members?