The capacity of an elevator is 10 people or 1560 pounds. The capacity will be ex

Question

The capacity of an elevator is 10 people or 1560 pounds. The capacity will be exceeded if 10 people have weights with a mean greater than 1560 divided by 10 equals 156 pounds.1560/10=156 pounds. Suppose the people have weights that are normally distributed with a mean of 163 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 156 pounds.

The probability is approximately [ ]. (Round to four decimal places as needed.)

b. Find the probability that 10 randomly selected people will have a mean that is greater than 156 pounds.

The probability is approximately [ ]. (Round to four decimal places as needed.)

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

A. No, there is a good chance that 10 randomly selected people will exceed the elevator capacity.

B. Yes, there is a good chance that 10 randomly selected people will not exceed the elevator capacity.

C. No, 10 randomly selected people will never be under the weight limit.

D. Yes, 10 randomly selected people will always be under the weight limit.

Explanation / Answer

a) P(X>156)=10P(Z<(156-163)/26)=1-P(Z<-0.2693)=1-0.3939=0.6061

b)for 10 people std error of mean =std deviation/(n)1/2 =8.2219

P(X>156)=10P(Z<(156-163)/8.2219)=1-P(Z<-8514)=1-0.1973=0.8027

c) A. No, there is a good chance that 10 randomly selected people will exceed the elevator capacity.

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