Question

The capacity of an elevator is 15 people or 2400 pounds. The capacity will be exceeded if 15 people have weights with a mean greater than 2400/15=160 pounds. Suppose the people have weights that are normally distributed with a mean of 167 lb and a standard deviation of 29 lb. find the probability that if a person is randomly selected, his weight will be greater than 160 pounds.

Answer 1

Answer:

0.5987

Step-by-step explanation:

$\mu = 167$

$\sigma = 29$

We are supposed to find the probability that if a person is randomly selected, his weight will be greater than 160 pounds.

Formula : $Z=\frac{x-\mu}{\sigma}$

P(x>160)

Substitute the values in the formula :

$Z=\frac{160-167}{29}$

$Z=−0.241$

Refer the z table for p value

p value = 0.4013

P(x>160)= 1-P(x<160)=1-0.4013=0.5987

Hence the probability that if a person is randomly selected, his weight will be greater than 160 pounds is 0.5987