Question

A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of

184184

lb and a standard deviation of

3636

lb. The gondola has a stated capacity of

2525

​passengers, and the gondola is rated for a load limit of

35003500

lb. Complete parts​ (a) through​ (d) below.

a. Given that the gondola is rated for a load limit of

35003500

​lb, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of

2525

​passengers?The maximum mean weight is

140140

lb.

​(Type an integer or a decimal. Do not​ round.)

b. If the gondola is filled with

2525

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

2020

passengers and the gondola is filled with

2020

randomly selected​ skiers, what is the probability that their mean weight exceeds

175175

​lb, which is the maximum mean weight that does not cause the total load to exceed

35003500

​lb?The probability is

​(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(-6.1111, 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(-1.1180, TRUE)" to find the probability.

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