# Probability in Managerial Decision-Making (Statistics Project Sample)

EXAMPLE:

Let’s suppose that the Goodyear Tire Company has just developed a tire to be sold. Since

the tire is new and Goodyear wants to introduce it into the consumer market, company

executives believe that a mileage guarantee offered with the tire will be an important factor

in buying the product. Goodyear managers want probability information about the number

of miles the tire will last.

From actual test data, Goodyear engineers estimate the mean (

X

) tire mileage to be:

μ = 36,500 miles

σ = 5,000 miles

A. What is the probability that tire mileage will exceed 40,000 miles?

Step1. At x = 40,000

5,000

3,500

5,000

40,000 36,500

x

z

.70

Step 2. The area to the left of .70 (listed in Table V on page A-11 in the appendix in your

text) is equal to .7580

Step 3. Subtract .7580 from 1.0 (the total area under the curve is equal to 1.0)

1.0 - .7580 = .2420

or

24.20% of the tires will exceed 40,000 in mileage

B. Let’s now assume that Goodyear is considering a guarantee that will provide a discount

on replacement tires if the original tires do not exceed the mileage in the guarantee. What

should the guaranteed mileage be if Goodyear wants no more than 10% of the tires to be

eligible for a discount?

The information we have available right now to help in this decision is that we have a

population mean of 36,500 with a standard deviation of 5,000. Goodyear management

wants no more than 10% of the tires to be eligible for a discount guarantee. If we draw a

normal distribution curve, 10% of the tires will fall in the lower left tail of the curve. Thus,

we are looking for the z-score value, such that the area to the left of this z-score under the

standard normal distribution curve is 10%, or 0.1000. Since the value 0.1000 does not

appear exactly in Table V, we use the closest value that is in the table, which is 0.1003. It

appears at the intersection of row -1.2 and column .08, which corresponds to the z-score of

-1.28.

To find the mileage of an unknown value of x that corresponds to a z = -1.28 we solve

algebraically:

Follow each step:

Method 1 or Method 2

1.28

x

z 1.28

5,000

36,500

x

1. x 1.28( )

1. x 36,500 1.28(5,000)

2. x 1.28( )

2. x 36,500 6,400

3. 30,100 = 36,500 – 1.28 (5,000) 3. x = 30,100

Either method to solve for x works. Use the method you’re most comfortable with.

A guarantee of 30,000 will meet the requirement that 10% of the tires will be eligible for

the guarantee.

From this example, we can see how probability can help the decision maker in reaching a

good decision.

QUESTION: After reading the example above where one can see how probability values can be used in managerial decision-making to establish a product guarantee, create a comment where you think probability could be used to help solve other management-type questions/problems. Think of something at work, past or present, where you could apply the techniques in the example to assist in making the best decision. If you can’t draw on a life experience, then think of a product/issue where this process could be applied. Please explain your answer.

Remember to cite your resources and use your own words in your explanation.

Probability in Managerial Decision-Making

Student`s Name

Institution

Date

Probability in Managerial Decision-Making

In any organization, a manager often deals with a situation where he has to choose between different alternatives. The problem with this choice is that the supporting information is often inadequate. Therefore there is some uncertainty associated with every managerial decision (Belton & Stewart, 2002). This is explained using the below example from personal experience.

A television manufacturer company wanted to introduce three different product variants (different in size- 43 inches, 50 inches, and 55 inches) in a new market. The company wanted to understand the demand for each variant and then plan the production accordingly.

The managerial dec

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