An elevator manufacturer has determined that a prototype model of elevator has a capacity to carry up to sixteen people and has an operating load of 3,200 pounds.
1) If there were sixteen people on the elevator, what would their mean weight need to be in order to equal the operating load of the elevator?
2) Assuming the people are all men and that men's weights are normally distributed with mean μ=172 lb and standard deviation σ=29 lb, what is the probability that a man chosen at random from the general population would have a weight in excess of the individual weight figured from part (1)?
3) What is the probability that the mean weight of sixteen randomly chosen men would exceed the individual weight from part (1)?
4) If the safety commission determines that an elevator design is safe if its operating load is exceeded less than 0.05% of the time, does this prototype meet these saftey guidelines?