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:0.5987Step-by-step explanation:[tex]\mu = 167[/tex][tex]\sigma = 29[/tex]We are supposed to find the probability that if a person is randomly selected, his weight will be greater than 160 pounds.Formula : [tex]Z=\frac{x-\mu}{\sigma}[/tex]P(x>160)Substitute the values in the formula :[tex]Z=\frac{160-167}{29}[/tex][tex]Z=−0.241[/tex]Refer the z table for p value p value = 0.4013P(x>160)= 1-P(x<160)=1-0.4013=0.5987Hence the probability that if a person is randomly selected, his weight will be greater than 160 pounds is 0.5987