SOLUTION: A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 190 lb and a standard deviation of 45 lb. The gondola h

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Question 1176271: A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 190 lb and a standard deviation of 45 lb. The gondola has a stated capacity of
25 passengers, and the gondola is rated for a load limit of 3500 lb.
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 probability that their mean weight exceeds
175 lb, which is the maximum mean weight that does not cause the total load to exceed
3500 lb?
What is the probability?

Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!

Hi Normal Distribution: μ = 190lbs σ = 45 25 passengers, gondola ...rated for a load limit of 3500 lb. x̄ = 140lb If: n = 20 passengers then x̄ = 175 P(x̄ > 175) = 1 - P( x̄ ≤ 175) t = (175 - 190)/(45/√20) = √20(-15)/45 = -1.4907 P(x̄ > 175) = 1 - P( x̄ ≤ 175) = 1 - P( t ≤ -1.4907, df19) = 1 - .0762 = .9238 Wish You the Best in your Studies.