ski gondola in Vail, Colorado, carries skiers to the top of a mountain. It bears a plaque stating that the maximum capacity is 12 people or 2004 That capacity will be exceeded if 12 people have weights with a mean greater than 2004/12 = 167 ib . Because men tend to weigh more than women, a worst case scenario involves 12 passengers who are all men. Assume that weights of men are normally distributed with a mean of 182.9 and a standard deviation of 40.8 lb. What is the probability that 12 randomly selected men will have a mean weight that is greater than 167 (so that their total weight is greater than the gondola maximum capacity of 2004 lb) ?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A ski gondola in Vail, Colorado, carries skiers to the top of a mountain. It bears a plaque stating that the maximum capacity is 12 people or 2004 That capacity will be exceeded if 12 people have weights with a mean greater than 2004/12 = 167 ib . Because men tend to weigh more than women, a worst case scenario involves 12 passengers who are all men. Assume that weights of men are normally distributed with a mean of 182.9 and a standard deviation of 40.8 lb. What is the probability that 12 randomly selected men will have a mean weight that is greater than 167 (so that their total weight is greater than the gondola maximum capacity of 2004 lb) ?
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