The capacity of an elevator is 15 people or 2370 pounds. The capacity will be ex

Question

The capacity of an elevator is 15 people or 2370 pounds. The capacity will be exceeded if 15 people have weights with a mean greater than 2370/15 158 pounds. Suppose the people have weights that are normally distributed with a mean of 168 Ib and a standard deviation of 30 lb. a. Find the probability that if a person is randomly selected, his weight will be greater than 158 pounds. The probability is approximately (Round to four decimal places as needed.) b. Find the probability that 15 randomly selected people will have a mean that is greater than 158 pounds. The probability is approximately Round to four decimal places as needed) c.Does the elevator appear to have the correct weight limit? Why or why not? O A. No, there is a good chance that 15 randomly selected people will exceed the elevator capacity O B. No. 15 randomly selected people will never be under the weight limit. O C. Yes, there is a good chance that 15 randomly selected people will not exceed the elevator capacity. D. Yes, 15 randomly selected people will always be under the weight limit.

Explanation / Answer

a) 158 lb is (158-158)/30 = .00 std dev below the mean; z = 0.00
From a z score table, p = .5000

b) For 15 people below 158
z = (158 - 168)/(30/sqrt(15) = -1.2910
p = .5000
For 12 people above 158 lb, p = 1 - .5000 = .5000

c) Answer C.

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