A ski gondola carries skiers to the top of a mountain. Assume that weights of sk

Question

A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 197 lb and a standard deviation of 44 lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3750 lb. Complete parts (a) through (d) below. a. Given that the gondola is rated for a load limit of 3750 lb, what is the maximum mean weight of the passengersif the gondola is filled to the stated capacity of 25 passengers? The maximum mean weight is 150 lb. (Type an integer or a decimal. Do not round.) b. If the gondola is filled with 25 randomly selected skiers, what is the probability that their mean weight exceeds the value from part (a)? The probability is 1 (Round to four decimal places as needed.) 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 probability that their mean weight exceeds 187.5 lb, which is the maximum mean weight that does not cause the total load to exceed 3750 lb? The probability is Round to four decimal places as needed.)

Explanation / Answer

a maximum mean weight=3750/25=150

b) P(Xbar>150)=P(Z>(150-197)/(44/sqrt(25))=P(Z>-5.34)=1.0000

c)

P(Xbar>187.5)=P(Z>(187.5-197)/(44/sqrt(20))=P(Z>-0.97)=0.8340

( please try 0.8329 if above comes wrong and revert)

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