Question 1099341:
The capacity of an elevator is 12 people or 2088 pounds. The capacity will be exceeded if 12 people have weights with a mean greater than 2088/12=174 pounds. Suppose the people have weights that are normally distributed with a mean of 180 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 174 pounds.
b. Find the probability that 12 randomly selected people will have a mean that is greater than 174 pounds.
c. Does the elevator appear to have the correct weight limit? Why or why not
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! z (174)>(174-180)/26
>=-6/26=-0.231
=0.5913
For 12 people, the sd is 26/sqrt(12)=7.51
that z is >-6/7.51, or probability=0.7878
It is a higher probability that the weight limit will be exceeded, because the sample of 12 has a distribution whose mean is closer to the population mean of 180. It is quite likely the elevator will be overloaded with 12 people.
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