A ski gondola carries passengers to the top of a mountain. Aplaque states that its maximum capacity is 12 people or 2019 lbs.Men’s weights are normally distributed with a mean of 179 lbs and astandard deviation of 30 lbs.
a)
What is the probability that 12 randomly-selected men willexceed the weight limit of the gondola?
b)
Suppose you are the engineer in charge of safety at themountain. What is the maximum number of men you would allow to ridethe gondola at a time in order to be confident they would notexceed the weight limit? Explain.
c)
Suppose the gondola carries the maximum number of men (as givenin part b) on every trip. The gondola operates for eight hours aday, and each trip takes 15 minutes to complete. What is theexpected amount of time before you lose your licence? Does thisanswer lead you to rethink your answer to part b)? If so, whatwould you do differently in part b) (you don’t have to redo partb)?
