   # Fuel Mileage Assume the fuel mileages of all 2015 model vehicles are normally distributed with a mean of 23.0 miles per gallon and a standard deviation of 5.7 miles per gallon. (Source: U.S. Environmental Protection Agency) (a) Use a graphing utility to graph the distribution. (b) Use a symbolic integration utility to approximate the probability that a vehicle’s fuel mileage is between 25 and 30 miles per gallon. (c) Use a symbolic integration utility to approximate the probability that a vehicle’s fuel mileage is less than 18 miles per gallon. ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919
Chapter 9.3, Problem 57E
Textbook Problem
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## Fuel Mileage Assume the fuel mileages of all 2015 model vehicles are normally distributed with a mean of 23.0 miles per gallon and a standard deviation of 5.7 miles per gallon. (Source: U.S. Environmental Protection Agency)(a) Use a graphing utility to graph the distribution.(b) Use a symbolic integration utility to approximate the probability that a vehicle’s fuel mileage is between 25 and 30 miles per gallon.(c) Use a symbolic integration utility to approximate the probability that a vehicle’s fuel mileage is less than 18 miles per gallon.

(a)

To determine

To graph: The provided normal probability density function by the use of a graphing utility if all the 2015 model vehicles are normally distributed with a mean of 23 and standard deviation of 5.7.

### Explanation of Solution

Given information:

For the normal probability density function the mean is μ=23 and standard deviation is σ=5.7

Graph:

The normal probability density function is given by

f(x)=1σ2πe(xμ)2(2σ2),<x<

Substitute μ=23 and σ=5.7 in the above equation,

f(x)=15.72πe(x23)22(5.7)2=0.0699e(x23)264

(b)

To determine

To calculate: The approximate probability that the vehicle’s fuel mileage is between 25 to 30 miles per gallon. by the use of symbolic integration utility.

(c)

To determine

To Calculate: The approximate probability that the vehicle’s fuel mileage is less than 18 miles per gallon. by the use of symbolic integration utility.

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