The capacity of an elevator is 8 people or 1264 pounds. The capacity will be exc

Question

The capacity of an elevator is 8 people or 1264 pounds. The capacity will be exceeded if 8people have weights with a mean greater than 1264 divided by 8 equals 158 pounds.1264/8=158 pounds. Suppose the people have weights that are normally distributed with a mean of 166 lb and a standard deviation of 26 lb. (a) Find the probability that if a person is randomly selected, his weight will be greater than 158 pounds. (b)Find the probability that 8 randomly selected people will have a mean that is greater than 158 pounds.

Explanation / Answer

= 166, = 26

(a) z = x - )/ = (158 - 166)/26 = -0.3077

P(x > 158) = P(z > -0.3077) = 0.6208

(b) z = (x - )/(/n) = (158 - 166)/(26/8) = -0.8703

P(x-bar > 158) = P(z > 0.8703) = 0.8079

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