A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 187 lb and a standard deviation of 45 lb. The gondola has a stated capacity of 25 passengers and is rated for a load limit of 3500 lb. Complete parts (a) through (d) below.

a. Given that the gondola is rated for a load limit of 3500 lb, what is the maximum mean weight per skier that allows the total weight not to exceed the limit?

The maximum mean weight per person that the ski gondola can carry, provided it has a total weight limit of 3500 lb and capacity for 25 passengers, is calculated as 140 lb per passenger.

Explanation:

To find the maximum mean weight per person that the gondola can carry, simply divide the total maximum load limit by the total number of passengers. So for this case, where the total load limit is 3500 lb and the passenger capacity is 25, we divide 3500 by 25.

Accordingly, the calculation would look like:

3500 lb / 25 passengers = 140 lb/passenger

This means that on average, each person in the gondola cannot weigh more than 140 lb if the gondola is to stay within its maximum load capacity of 3500 lb. Please remember this is a theoretical average - actual weights will vary and it's advisable not to exceed maximum stated capacities in order to maintain safety.

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