Question

Elevator ride: Engineers are designing a large elevator that will accommodate 43 people. The maximum weight the elevator can hold safely is 8643 pounds. According to the National Health Statistics Reports, the weights of adult U.S. men have mean 189 pounds and standard deviation 63 pounds, and the weights of adult U.S. women have mean 170 pounds and standard deviation 72 pounds. Use the TI-84 Plus calculator.

(a) If 43 people are on the elevator, and their total weight is 8643 pounds, what is their average weight?

(b) If a random sample of 43 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

(c) If a random sample of 43 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.

Answer 1

Given that,

For men : mean = 189 pounds and sd = 63 pounds

For women : mean = 170 pounds and sd = 72 pounds.

a) sample size = 43 and total weight = 8643 pounds

=> Average weight = 8643/43 = 201 pounds

b) Using TI-83 plus calculator we get, P(x-bar > 201) for men.

P(x-bar > 201) = 0.105826

Therefore, required probability is 0.105826

c)

Using TI-83 plus calculator we get, P(x-bar > 201) for women.

P(x-bar > 201) = 0.002376

Therefore, required probability is 0.002376