Question

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

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 42 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 ____ 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 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.)

d. Is the new capacity of 20 passengers​ safe?

Since the probability of overloading is EITHER under 5% / over 50% , the new capacity EITHER does not appear / does appear to be safe enough.

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