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# Analyzing Ford F-750 Mileage Using Z-Scores & Probabilities

**Chapter 0, Problem 54**

(choose chapter or problem)

**QUESTION:**

Fast Service Truck Lines uses the Ford Super Duty F-750 exclusively. Management made a study of the maintenance costs and determined the number of miles traveled during the year followed the normal distribution. The mean of the distribution was 60,000 miles and the standard deviation 2,000 miles.

a. What percent of the Ford Super Duty F-750s logged 65,200 miles or more?

b. What percent of the trucks logged more than 57,060 but less than 58,280 miles?

c. What percent of the Fords traveled 62,000 miles or less during the year?

d. Is it reasonable to conclude that any of the trucks were driven more than 70,000 miles? Explain

### Questions & Answers

**QUESTION:**

Fast Service Truck Lines uses the Ford Super Duty F-750 exclusively. Management made a study of the maintenance costs and determined the number of miles traveled during the year followed the normal distribution. The mean of the distribution was 60,000 miles and the standard deviation 2,000 miles.

a. What percent of the Ford Super Duty F-750s logged 65,200 miles or more?

b. What percent of the trucks logged more than 57,060 but less than 58,280 miles?

c. What percent of the Fords traveled 62,000 miles or less during the year?

d. Is it reasonable to conclude that any of the trucks were driven more than 70,000 miles? Explain

**ANSWER:**

Step 1 of 4

The mean of the distribution, \(\mu=60,000\)

The standard deviation, \(\sigma=2,000\)

The z-value represents the signed distance between a selected value, designated \(X\), and the mean divided by the standard deviation, ie;

\(z=\frac{X-\mu}{\sigma}\)

Where, \(X\) is the value of any particular observation or measurement

Calculate the z-value for the Ford Super Duty F-750s logged 65,200 miles,

\(z=\frac{65200-60000}{2000}=2.6\)

We know that the area under the normal distribution curve to the right of the z-value, 2.6 represents the percent of the Ford Super Duty F-750s logged 65,200 miles or more. Using the table in Appendix B.1 the probability for the standard normal probability distribution, with z-value = 2.6 is

\(P(z>2.6)=0.5-0.4953=0.0047\)

Therefore the percent of the Ford Super Duty F-750s logged 65,200 miles or more is 0.47%

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##### Analyzing Ford F-750 Mileage Using Z-Scores & Probabilities

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Explore how z-scores help analyze the mileage of Ford Super Duty F-750 trucks. Discover the percentages that reached specific mileage markers and grasp the significance of data using the z-table.