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Answer :
The problem describes a ski gondola with a stated capacity of 25 passengers and a load limit of 3750lb. The weights of skiers are normally distributed with a mean of 197lb and a standard deviation of 43lb.
To find the maximum mean weight of the passengers, we need to calculate the total weight that the gondola can handle based on its load limit and the number of passengers. Since the load limit is 3750lb and the stated capacity is 25 passengers, we divide the load limit by the number of passengers to obtain the maximum allowable weight per passenger:
Maximum allowable weight per passenger = 3750lb / 25 passengers = 150lb. This means that, if the gondola is filled to its stated capacity of 25 passengers, the maximum mean weight of the passengers cannot exceed 150lb.
If the mean weight were higher than 150lb, the total weight of the passengers would exceed the load limit of the gondola, which could be unsafe. Therefore, the maximum mean weight of the passengers, under the given conditions, is 150lb.
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