A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 200 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 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 Ib. (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 Li 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 Ib? The probability is- pti (Round to four decimal places as needed.) Is d. Is the new capacity of 20 passengers safe? Since the probability of overloading is V the new capacity to be safe enough.
A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 200 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 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 Ib. (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 Li 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 Ib? The probability is- pti (Round to four decimal places as needed.) Is d. Is the new capacity of 20 passengers safe? Since the probability of overloading is V the new capacity to be safe enough.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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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 200 lb 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 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
Ib.
(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
Li 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 Ib?
The probability is-
pti
(Round to four decimal places as needed.)
Is
d. Is the new capacity of 20 passengers safe?
Since the probability of overloading is
V the new capacity
to be safe enough.
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