1. 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 28-lbs. An elevator in the health club is limited to 35 occupants, but it will be overloaded if the total weight is in excess of 6300-lbs. Assume that there are 35 men in the elevator. What is the average weight of the 35 men 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 35 male occupants in the elevator are the result of a random selection, find the probability that the elevator will be overloaded? P(elevator overloaded) = (Report answer accurate to 4 decimal places.) If the elevator is full (on average) 4 times a day, how many times will the elevator be overloaded in one (non-leap) year? number of times overloaded = (Report answer rounded to the nearest whole number.)

2. A manufacturer knows that their items have a normally distributed length, with a mean of 14.9 inches, and standard deviation of 4.3 inches. If 9 items are chosen at random, what is the probability that their mean length is less than 11.6 inches? Round your answer to four decimal places.