Probability/Statistics

The capacity of a lift is 12 people or 2028 pounds. The capacity will be exceeded if 12 people have weights with a mean greater than 2028/22=169 pounds. Suppose the people have weights that are normally distributed with a mean of 176pounds and a standard deviation of 33 pounds

A. Find the probability that if a person is randomly selected, his weight will be greater than 169 pounds
B. Find the probability that 12 randomly selected people will have a mean that is greater than 169 pounds

part a, just use \(\displaystyle z=\frac{x-{\mu}}{\sigma}\) and look up the value in the z table. Since they want > 169, subtract the value you find from 1.

part b, same as above except use \(\displaystyle z=\frac{(x-{\mu})\sqrt{n}}{\sigma}\)


\(\displaystyle x=169, \;\ {\mu}=176, \;\ {\sigma}=33, \;\ n=12\)