Question

A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 201 lb and a standard deviation of 43 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 passengers if 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 11.
​(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 nothing.
​(Round to four decimal places as​ needed.)

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(-5.9302, TRUE)" to find the probability.

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Given: n=20

Refer Standard normal table/Z-table to find the probability or use excel formula "=NORM.S.DIST(-1.4040, TRUE)" to find the probability.

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