Question

2. A ski gondola in Vail, CO, carries skiers to the top of a mountain. It bears a plaque stating the maximum capacity is 12 people of 2004 pounds. That capacitywill be exceeded if 12 people have weights with a mean greater than 2004/12 = 167 pounds. Because men tend to weigh more than women, a “worse case” scenarioinvolves 12 passengers who are all men. Men have weights that are normally distributed with a mean of 172 pounds with a standard deviation of 29 pounds (based ondata from the National Health Survey).
a. Find the probability that if an individual man is randomly selected, his weight will be greater than 167 pounds.

b. Find the probability that 12 randomly selected men will have a mean that is greater than 167 pounds (so that their total weight is greater than the gondolamaximum capacity of 2004 pounds).

Answer 1

a. P(X>167) = P((X-mean)/s >(167-172)/29)
=P(Z>-0.17)
= 0.5675 (check standard normal table)

b. P(xbar>167)
=P((xbar-mean)/(s/vn) >(167-172)/(29/sqrt(12)))
=P(Z> -0.6)
= 0.7257 (check standard normal table)