The capacity of an elevator is 10 people or 1610 pounds. The capacity will be ex

Question

The capacity of an elevator is 10 people or 1610 pounds. The capacity will be exceeded if 10 people have weights with a mean greater than 1610 divided by 10 equals 161 pounds.1610/10=161 pounds. Suppose the people have weights that are normally distributed with a mean of 163 lb and a standard deviation of 27 lb. a. Find the probability that if a person is randomly selected, his weight will be greater than 161 pounds. Find the probability that 10 randomly selected people will have a mean that is greater than 161 pounds.

Explanation / Answer

a) For Single person

P(X>161)

P(Z>(161-163)/27)

P(Z>-0.0741)

= 0.5295 (rounded to four decimal places)

b) For 10 People

P(X>161)

P(Z>((161-163)/27))*Sqrt(10)

P(Z>-0.2342)

= 0.5926 (rounded to four decimal places)

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