An elevator has a placard stating that the maximum capacity is 2505 lb15 passengers.So, 15 adult male passengers can have a mean weight of up to 2505/15=167pounds. If the elevator is loaded with 15 adult malepassengers, find the probability that it is overloaded because they have a mean weight greater than 167 lb.(Assume that weights of males are normally distributed with a mean of 170lb and a standard deviation of 33lb.) Does this elevator appear to besafe?

Before everyflight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 37 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6,031 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 6,031lb37=163 lb. What is the probability that the aircraft isoverloaded? Should the pilot take any action to correct for an overloadedaircraft? Assume that weights of men are normally distributed with a mean of 180.2 lb and a standard deviation of 39.1.

The overhead reach distances of adult females are normally distributed with a mean of 205.5cm and a standard deviation of 8.9cm.

a. Find the probability that an individual distance is greater than 214.80 cm.

b. Find the probability that the mean for 15 randomly selected distances is greater than 204.20cm.

c. Why can the normal distribution be used in part(b), even though the sample size does not exceed30?