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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 38 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 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 38 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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
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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 38 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 Ib, 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 probability that their mean weight exceeds 175 lb, which is the maximum mean weight that does not cause the total load to exceed 3500 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 V the new capacity V to be safe enough.
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 38 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 Ib, 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 probability that their mean weight exceeds 175 lb, which is the maximum mean weight that does not cause the total load to exceed 3500 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 V the new capacity V to be safe enough.
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