The capacity of an elevator is 15 people or 2296 pounds. The capacity wil be exc

Question

The capacity of an elevator is 15 people or 2296 pounds. The capacity wil be exceeded if 15 people have weights with a mean greater than 2295/15 153 pounds. Suppose the peopie have weights that are normally distributed with a mean of 161 lb and a standard deviation of 35 Ib a. Find the probablity that if a person is randomly selected, his weight will be greater than 153 pounds. The probablity is accronmately (Rond to fur dearnal places as needed ) b. Find the probability that 15 randomly selected people will have a mean that is greater than 153 pounds Theprobablity is approimaiity(Round tolour domal places as needed) O A. Yes, 15 randomly selected people will ahways be under the weight liit O B. No. 15 randomly selected people will never be under the weight mit OC. No. thoro agood chance that 15 randomly selected people will exceed the elevator capacity O D. Yes, there is a good chance that 15 randomly selected people will not exceed the elevator capacity

Explanation / Answer

a)P(X>153)=P(Z>(153-161)/35)=P(Z>-0.2286)=0.5904

b) for n=15 ; std error of mean =std deviation/(n)1/2 =35/sqrt(15) =9.037

therefore P(X>153)=P(Z>(153-161)/9.037)=P(Z>-0.8853)=0.8120

c)

option C is correct

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