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Answer :
Answer:
0.57926
Step-by-step explanation:
We have been given that the capacity of an elevator is 15 people or 2385 pounds. The people have weights that are normally distributed with a mean of 165 lb and a standard deviation of 30 lb. We are asked to find the probability that a randomly selected person has a weight greater than 159 pounds.
First of all, we will find z-score corresponding to 159 using z-score formula.
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{159-165}{30}[/tex]
[tex]z=\frac{-6}{30}[/tex]
[tex]z=-0.2[/tex]
Now, we need to find area under normal distribution curve that is greater than z-score of [tex]-0.2[/tex] as: [tex]P(z>-0.2)[/tex]
Using formula [tex]P(z>a)=1-P(z [tex]P(z>-0.2)=1-P(z<-0.2)[/tex] [tex]P(z>-0.2)=1-0.42074[/tex] [tex]P(z>-0.2)=0.57926[/tex] Therefore, the probability that if a person is randomly selected, his weight will be greater than 159 pounds, is 0.57926.
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