Engineers are designing a large elevator that will accommodate 42 people. The maximum weight the elevator can hold safely is 8148 pounds. According to the National Health Statistics Reports, the weights of adult U. S. men have mean 188 pounds and standard deviation 63 pounds, and the weights of adult U. S. women have mean 158 pounds and standard deviation 72 pounds. (a) If 42 people are on the elevator, and their total weight is 8148 pounds, what is their average weight? The average weight is pounds.
(b) If a random sample of 42 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded? Round the answer to at least four decimal places. The probability that the maximum safe weight will be exceeded is
(c) If a random sample of 42 adult women ride the elevator, what is the probability that the maximum safe weight will be exceeded? Round the answer to at least four decimal places.