Question

The capacity of an elevator is 15 people or 2475 pounds. The capacity will be exceeded...

The capacity of an elevator is 15 people or 2475 pounds. The capacity will be exceeded if 15 people have weights with a mean greater than 2475/15=165 pounds. Suppose the people have weights that are normally distributed with a mean of 170 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 165 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 165 pounds.

c. Does the elevator appear to have the correct weight limit? Why or why not?

Math   Statistics-And-Probability   
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Answer #1

The people have weights that are normally distributed with a mean of 170 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 165 pounds

z(165)=(165-170)/26=-0.192

P(Z>-0.192)=0.5761 ......from z table

b. Find the probability that 15 randomly selected people will have a mean that is greater than 165 pounds

P(Z>-0.7448)=0.7727

c. Does the elevator appear to have the correct weight limit? Why or why not?

No,There is a good chance 15 selected people elevator exceed the limit

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