The capacity of an elevator is 12 people or 2124 pounds. The capacity will be ex

Question

The capacity of an elevator is 12 people or 2124 pounds. The capacity will be exceeded if 12 people have weights with a mean greater than 2124 divided by 12 equals 177 pounds. 2124/12=177 pounds. Suppose the people have weights that are normally distributed with a mean of 180 lb and a standard deviation of 35 lb. a. Find the probability that if a person is randomly selected, his weight will be greater than 177 pounds. The probability is approximately nothing . (Round to four decimal places as needed.) b. Find the probability that 12 randomly selected people will have a mean that is greater than 177 pounds. The probability is approximately nothing . (Round to four decimal places as needed.) c. Does the elevator appear to have the correct weight limit? Why or why not? A. No, 12 randomly selected people will never be under the weight limit. B. Yes,12 randomly selected people will always be under the weight limit. C. No, there is a good chance that 12 randomly selected people will exceed the elevator capacity. D. Yes, there is a good chance that 12 randomly selected people will not exceed the elevator capacity.

Explanation / Answer

= 180, = 35

(a) z = (177 - 180)/35 = -0.0857

P(x > 177) = P(z > -0.0857) = 0.5342

(b) z = (177 - 180)/(35/12) = -0.2969

P(x-bar > 177) = P(z > -0.2969) = 0.6167

(c) C. No, there is a good chance that 12 randomly selected people will exceed the elevator capacity

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