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For a particular elevator, the average weight of a person who enters the elevator is 165.347 pounds (lbs), with a standard deviation of 22.046 lbs.
(a) Find the probability that the average weight of 36 people entering the elevator is above 170 lbs.
(b) Assume the population is normally distributed. What is the probability that the total weight of 16 people is over 2500 lbs?
(c) Assume the population is normally distributed. What is the probability that the total weight of 16 people is over 3500 lbs?
(d) If the sign on the elevator says "Maximum capacity X lbs or 16 people", and you had to decide which weight X (2500 or 3500 lbs) to list, which would you choose based on (b) and (c) to ensure the elevator would rarely fail? Explain your answer.
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