Question

Elevator ride: Engineers are designing a large elevator that will accommodate 56 people. The maximum weight the elevator can hold safely is 11,144

pounds. According to the National Health Statistics Reports, the weights of adult U.S. men have mean 196 pounds and standard deviation 71 pounds, and the weights of adult U.S. women have mean 169 pounds and standard deviation 80 pounds. Use the TI-84 Plus calculator.

Part 1 of 3

(a) If 56 people are on the elevator, and their total weight is 11,144 pounds, what is their average weight?

The average weight is pounds.

Part 2 of 3

(b) If a random sample of 56 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 .

Part 3 of 3

(c) If a random sample of 56 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.

The probability that the maximum safe weight will be exceeded is .

Answer 1

a)

b) Let X be a random variable representing  the weights of adult U.S. men. Then,

Then, for 56 adult men,

Hence, the probability that the maximum safe weight will be exceeded

c) Let Y be a random variable representing  the weights of adult U.S. women. Then,

Then, for 56 adult men,

Hence, the probability that the maximum safe weight will be exceeded