NOTE: Answers using z-scores rounded to 3 (or more) decimal places will work for this problem. The population of weights for men attending a local health club is normally distributed with a mean of 168-lbs and a standard deviation of 27-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 5792-lbs. Assume that there are 32 men in the elevator. What is the average weight beyond which the elevator would be considered overloaded? average weight = lbs What is the probability that one randomly selected male health club member will exceed this weight? P(one man exceeds) = (Report answer accurate to 4 decimal places.) If we assume that 32 male occupants in the elevator are the result of a random selection, find the probability that the evelator will be overloaded? P(elevator overloaded) = (Report answer accurate to 4 decimal places.) If the evelator is full (on average) 7 times a day, how many times will the evelator be overloaded in one (non-leap) year? number of times overloaded = (Report answer rounded to the nearest whole number.) 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