What is the probability the elevator is overloaded?

Question

An elevator has a placard stating that the maximum capacity is 2016 lb- 12 passengers.​ So, 12 adult male passengers can have a mean weight of up to 2016/12=168 pounds If the elevator is loaded with 12 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 168 lb.​ (Assume that weights of males are normally distributed with a mean of 174 lb and a standard deviation of 31 lb​.) Does this elevator appear to be​ safe?

Answer 1

P(xbar > 168) = P(z > (xbar - mu)/(SD/sqrt(sample size)) = P(z < (168 - 174)/(31/sqrt(12) = P(z > -0.67) = P(z < 0.67) = 0.7486