Question

A ski gondola carries skiers to the top of the mountain. Assume the weights of the skiers are normally distributed with a mean of 198 lb and a standard deviation of 35 lb. The gondola has a stated capactiy of 25 passengers and the gondola is rated for a load limit of 3750 lbs Complete parts a-d

a. Given the gondola is rated for a load limit of 3750 lb what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 passengers the maximum mean weight is?

b. If the gondola is filled with 25 randomly selected skiers what is the probablity that their mean weight exceeds the value from part A?

c If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is filled with 20 randomly selected skiers, what is the probablity that their mean weight exceeds 187.5 lbs which is the maximum mean weight that does not cause the total load to exceeed 3750 lbs.

d.Is the new capacity of 20 passengers safe?

Answer 1

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Given: n=25

Refer Standard normal table/Z-table to find the probability or use excel formula "=NORM.S.DIST(-6.8571, TRUE)" to find the probability.

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Refer Standard normal table/Z-table to find the probability or use excel formula "=NORM.S.DIST(-1.3416, TRUE)" to find the probability.

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