Question

A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 189lb and a standard deviation of 38lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3500lb. Complete parts (a) through (d) below.

a. Given that the gondola is rated for a load limit of 3500lb, 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 ________ 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?  (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 175lb, which is the maximum mean weight that does not cause the total load to exceed 3500lb?

The probability is? (Round to four decimal places as needed.)

d. Is the new capacity of 20 passengers safe?

Since the probability of overloading is (1)_______ the new capacity (2)________ to be safe enough.

(1) under 5%, over 50%, (2) does not appear, appears

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(-6.45, 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(-1.6476, TRUE)" to find the probability.

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