Question

Engineers are designing a large elevator that will accommodate 58 people. The maximum weight the elevator can hold safely is pounds. According to the National Health Statistics Reports, the weights of adult U.S. men have mean pounds and standard deviation pounds, and the weights of adult U.S. women have mean pounds and standard deviation pounds. Use the TI-84 Plus calculator.
Required:
a. If 58 people are on the elevator, and their total weight is 11,716 pounds, what is their average weight?
b. If a random sample of 58 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?

Answer 1

Complete question is;

Engineers are designing a large elevator that will accommodate 58 people. The maximum weight the elevator can hold safely is 11,716 pounds. According to the National Health Statistics Reports, the weights of adult U.S. men have mean 190 pounds and standard deviation 62 pounds, and the weights of adult U.S. women have mean 184 pounds and standard deviation 71 pounds. Use the TI-84 Plus calculator.

Required:

a. If 58 people are on the elevator, and their total weight is 11,716 pounds, what is their average weight?

b. If a random sample of 58 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?

Answer:

A) average weight = 202 pounds

B) the probability that the maximum safe weight will be exceeded = 42.47%

Step-by-step explanation:

A) We are told that 58 people are on the elevator and that their total weight is 11,716 pounds. Thus;

Average weight = total weight/number of people = 11716/58 = 202 pounds

B) We will use z-score formula in this;

z = (x¯ - μ)/σ

Now, in part a above, we saw that the average weight is 202 pounds. Thus; x¯ = 202 pounds

We are told that standard deviation for men is;

σ = 62 pounds

We are told that the weights of adult U.S. men have mean 190 pounds . Thus; μ = 190

Thus;

z = (202 - 190)/62

z = 0.19

From z-distribution table, p-value = 0.57535

Thus;

P(z > 0.19) = 1 - 0.57535 = 0.42465

Thus, the probability that the maximum safe weight will be exceeded = 0.42465 ≈ 42.47%