Chapter 6.4, Problem 28E

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10th Edition

Ron Larson

ISBN: 9781305860919

Textbook Problem

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**HOW DO YOU SEE IT?** The graph shows the probability density function for a car brand that has a mean fuel efficiency of 26 miles per gallon and a standard deviation of 2.4 miles per gallon.

(a) Which is greater, the probability of choosing a car at random that gets between 26 and 28 miles per gallon or the probability of choosing a car at random that gets between 22 and 24 miles per gallon?

(b) Which is greater, the probability of choosing a car at random that gets between 20 and 22 miles per gallon or the probability of choosing a car at random that gets at least 30 miles per gallon?

**(a)**

To determine

Whether the probability of choosing a car at random that gets between 26 and 28 miles per gallon is greater or that gets between 22 and 24 miles per gallon is greater.

Explanation

**Given Information:**

The probability density function for a car brand having standard deviation of

Use excel to find the probability. Steps to use excel is as follows:

Calculation of the probability for the cars which gives mileage between

Step 1: Add the function “NORM.DIST” in the excel.

Step 2: Add the values of the “*x*”, mean, standard deviation and cumulative as “=NORM.DIST(26,26,2.4, TRUE)” in the cell as shown in the below snip.

Step 3: Once you press enter, the result is obtained as the result is for the

Therefore, the probability for

Step 4: Add the values of the “*x*”, mean, standard deviation and cumulative as “=NORM.DIST(28,26,2.4, TRUE)” in the cell as shown in the below snip.

Step 5: Once you press enter, the result is obtained as the result is for the

Therefore, the probability for

Therefore, probability for the car efficiency between

Calculation of the probability for the cars which gives mileage between

**(b)**

To determine

Whether the probability of choosing a car at random that gets between 20 and 22 miles per gallon is greater or that gets at least 30 miles per gallon is greater.

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