The population of weights for men attending a local health club is normally distributed with a mean of 166-lbs and a standard deviation of 31-lbs. An elevator in the health club is limited to 32 occupants, but it will be overloaded if the total weight is in excess of 5696-lbs. Assume that there are 34 men in the elevator.

What is the average weight per man beyond which the elevator would be considered overloaded?

average weight = lbs Round to the nearest pound.

What is the probability that one randomly selected male health club member will exceed this weight?

P(one man exceeds) = Round to 4 decimal places.

If we assume that 34 male occupants in the elevator are a random sample of all male club members, find the probability that the elevator will be overloaded?

P(elevator overloaded) = Round to 4 decimal places.

If the elevator is full (on average) 5 times a day, how many times do we expect the elevator will be overloaded in one (non-leap) year?

number of times overloaded = Round to the nearest day.

Is there reason for concern?

no, the current overload limit is adequate to insure the safety of the passengers

yes, the current overload limit is not adequate to insure the safey of the passengers