A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 180 and a standard deviation of 36 Ib. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit 3500 lb. Complete parts (a) through (d) below. a. Given that the gondola is rated for a load limit of 3500 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 140 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.)

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A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 180 lb
and a standard deviation of 36 lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of
3500 lb. Complete parts (a) through (d) below.
a. Given that the gondola is rated for a load limit of 3500 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 140 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.)
Transcribed Image Text:A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 180 lb and a standard deviation of 36 lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3500 lb. Complete parts (a) through (d) below. a. Given that the gondola is rated for a load limit of 3500 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 140 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.)
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