A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 190 lb and a standard deviation of 44 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 1.0000. (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 Ib? The probability is: (Round to four decimal places as needed.)

A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 190 lb and a standard deviation of 44 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 1.0000. (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 Ib? The probability is: (Round to four decimal places as needed.)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 190 lb and a standard deviation of 44 lb. The gondola has a stated
capacity of 25 passengers, and the gondola is rated for a load limit of 3500 Ib. 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 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 1.0000
(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 Ib, which is the maximum mean weight that does not cause the total load to exceed 3500 Ib?
The probability is
(Round to four decimal places as needed.)

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