The capacity of an elevator is 8 people or 1280 pounds. The capacity will be exc

Question

The capacity of an elevator is 8 people or 1280 pounds. The capacity will be exceeded if 8 people have weights with a mean greater than 1280/ 8= 160 pounds. Suppose the people have weights that are normally distributed with a mean of 170 lb and a standard deviation of 32 lb.

a. Find the probability that if a person is randomly? selected, his weight will be greater than 160 pounds.

b. Find the probability that 8 randomly selected people will have a mean that is greater than 160 pounds.

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

Explanation / Answer

a) P(z>(160-170)/32)

= P(z>-0.3125)

= 0.6227

b) P(z>((160-170)/32)*SQRT(8)

= P(z>-0.8839)

= 0.8116

c) Yes, because probabilities are very large

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