The population of weights for men attending a local health club is normally distributed with a mean of 172-lbs and a standard deviation of 27-lbs. An elevator in the health club is limited to 33 occupants, but it will be overloaded if the total weight is in excess of 6105-lbs.

(a)Assume that there are 33 men in the elevator. What is the average weight beyond which the elevator would be considered overloaded?

average weight =lbs

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

P(one man exceeds) =

Round answer to 4 decimal places.

(c)If we assume that 33 male occupants in the elevator are the result of a random selection, find the probability that the evelator will be overloaded?

P(elevator overloaded) =

Round answer to 4 decimal places.

(d)If the evelator is full (on average) 7 times a day, how many times will the elevator be overloaded in one (non-leap) year?

number of times overloaded =

Round answer to the nearest whole number.

(e)Is there reason for concern?

• yes, the current overload limit is not adequate to insure the safey of the passengers
• no, the current overload limit is adequate to insure the safety of the passengers