Introduction to Management Science (10th Edition)

[Page 504 ( continued )]

The following example will illustrate the solution of a problem involving a normal probability.

Problem Statement

The Radcliffe Chemical Company and Arsenal produces explosives for the U.S. Army. Because of the nature of its products, the company devotes strict attention to safety, which is also scrutinized by the federal government. Historical records show that the annual number of property damage and personal injury accidents is normally distributed, with a mean of 8.3 accidents and a standard deviation of 1.8 accidents.

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  1. What is the probability that the company will have fewer than 5 accidents next year? more than 10?

  2. The government will fine the company $200,000 if the number of accidents exceeds 12 in a 1-year period. What average annual fine can the company expect?

Solution

Step  1.

Set Up the Normal Distribution

Step  2.

Solve Part A

From Table A.1 in Appendix A we see that Z = 1.83 corresponds to a probability of .4664; thus,

From Table A.1 in Appendix A we see that Z = .94 corresponds to a probability of .3264; thus,

P ( x 10)

=

.5000 .3264

 

=

.1736

Step  3.

Solve Part B

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From Table A.1 in Appendix A we see that Z = 2.06 corresponds to a probability of .4803; thus,

Therefore, the company's expected annual fine is

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