A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 194 lb and a standard deviation of 45 lb. The gondola has a stated capacity...

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

194

lb and a standard deviation of

lb. The gondola has a stated capacity of

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

passengers?

The maximum mean weight is

nothing

lb.

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

b. If the gondola is filled with

randomly selected skiers, what is the probability that their mean weight exceeds the value from part (a)?

The probability is

nothing.

(Round to four decimal places as needed.)

c. If the weight assumptions were revised so that the new capacity became

passengers and the gondola is filled with

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.)

d. Is the new capacity of

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

Jun 04, 2022

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