Answered: The Age of Disposability. Suppose that…

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

The Age of Disposability. Suppose that the life of a certain device is approximately normally distributed with mean 48 months and standard deviation 16 months. You must use the product for 2 years. If it fails in that period, your cost will be $1000. If it does not fail, your cost will be $500. Type calculations/explanations in answering all these questions:

a) What proportion of these devices are expected to fail during the 2-year use period?

b) What is your expected cost of using this device for the 2 years?

c) Approximately, what would be a fair price for a warranty against failure in the 2-year period?

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.

Expert Solution

Step 1

Let X be the random variable denoting the life of the device (in months). Then the given information is:

$X ~ N o r m a l (μ = 48, σ^{2} = 16^{2})$

The two costs associated with the device are:

1. If the product fails before 2 years (that is X<24), the cost is $1000

2. If the product does not fail before 2 years (X>24), the cost is $500

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