Answered: A ski gondola carries skiers to the top…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of

194

lb and a standard deviation of

lb. The gondola has a stated capacity of

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

passengers?

The maximum mean weight is

nothing

lb.

(Type an integer or a decimal. Do not round.)

b. If the gondola is filled with

randomly selected skiers, what is the probability that their mean weight exceeds the value from part (a)?

The probability is

nothing.

(Round to four decimal places as needed.)

c. If the weight assumptions were revised so that the new capacity became

passengers and the gondola is filled with

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

nothing.

(Round to four decimal places as needed.)

d. Is the new capacity of

passengers safe?

Since the probability of overloading is

(1)

the new capacity

(2)

to be safe enough.

(1)

under 5%,

over 50%,

(2)

does not appear

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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