1. A ski gondola in Vail, Colorado carries skiers to the top of the mountain. Th
ID: 3321399 • Letter: 1
Question
1. A ski gondola in Vail, Colorado carries skiers to the top of the mountain. The faceplate on the equipment states that the maximum capacity is 12 people or 2004 lb. The average weight of a passenger at these values is 167 lb. Because men tend to weigh more than women, the worst case loading scenario would involve 12 passengers who are all men. Assume that weights of men are normally distributed with a mean of 182.8 lb and a standard deviation of 40.8 lb. (a) Find the probability that if an individual man is randomly selected, his weight will be greater than 167 lb. (b) Find the probability that the 12 randomly selected men will have a mean weight that is greater than 167 lb (so that their total weight is greater than the gondola faceplate rating of 2004 lb. ) Does the gondola appear to have correct weight limits? If not, what would be a quick fix for the problem?Explanation / Answer
a) Mean = 182.8
SD = 40.8
z = (167 - 182.8)/40.8
z = - 0.387
P = 0.6480
b) This is a normal distributionsince the original distribution is. Therefore the mean is same
However, the new standard deviation is/sqrt(n) = 40.8/sqrt(12) = 11.78
z = (167 - 182.8)/11.78
z = - 1.34
P = 0.9099
c) No. It appears that the 12-person capacity could easily exceed the 2004 pounds. (Of course you'd also have to ask whether the weight of a typical skier is representative a typical man's weight from the total population, as skiers might be more fit.)
The weight of men before the process starts could be weighed so that there is not a case of over weight
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