An elevator has a placard stating that the maximum capacity is 1980 lb—12 passengers.​ So, 12 adult male passengers can have a mean weight of up to 1980/12=165 pounds. If the elevator is loaded with...

An elevator has a placard stating that the maximum capacity is

1980

lb—12

passengers.​ So,

12

adult male passengers can have a mean weight of up to

1980/12=165 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

165

lb.​ (Assume that weights of males are normally distributed with a mean of

171 lb

and a standard deviation of

35 lb​.)

Does this elevator appear to be​ safe?