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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

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.

Chapter 6.4, Problem 28E, HOW DO YOU SEE IT? The graph shows the probability density function for a car brand that has a mean

(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 2.4 miles per gallon and mean fuel efficiency of 26 miles per gallon is shown below by the graph,

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

Calculation of the probability for the cars which gives mileage between 26 miles per gallon to 28miles per gallon.

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 0 to 26 miles per gallon.

Therefore, the probability for

P(0x26)=0.5

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 0 to 28miles per gallon.

Therefore, the probability for

P(0x28)=0.79767

Therefore, probability for the car efficiency between 26miles per gallon and 28miles per gallon are:

P(26x28)=P(0x28)P(0x26)=0.797670.5=0.29767

Calculation of the probability for the cars which gives mileage between 22miles per gallon to 24miles per gallon

(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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