USE CENTRAL LIMIT THEOREM

Part 1:

A ski gondola carries skiers to the top of a mountain. Assume that the total weights of adult skiers (including their equipment) are normally distributed with a mean of 200 lb and a standard deviation of 40 lb. Further assume that the gondola can carry a maximum of 25 skiers and has a maximum load limit of 5,000 lb. If the gondola is full, it will be overloaded if the mean total weight of the skiers exceeds 5,000 lb / 25 skiers = 200 lb/skier. If the gondola is filled with 25 randomly selected skiers, what is the probability that it will be overloaded? (Round your answer to three decimal places; add trailing zeros as needed.)

The probability that 25 randomly selected skiers will overload the gondola is?

Part 2:

Consider the ski gondola from Question 3. Suppose engineers decide to reduce the risk of an overload by reducing the passenger capacity to a maximum of 15 skiers. Assuming the maximum load limit remains at 5,000 lb, what is the probability that a group of 15 randomly selected skiers will overload the gondola? (Round your answer to three decimal places; add trailing zeros as needed.)

The probability that 15 randomly selected skiers will overload the gondola is?