Q 79. In its Fuel Economy Guide for 20... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 3: Q 79. (page 197)

In its Fuel Economy Guide for $2008$ model vehicles, the Environmental Protection Agency gives data on $1152$ vehicles. There are a number of outliers, mainly vehicles with very poor gas mileage. If we ignore the outliers, however, the combined city and highway gas mileage of the other $1120$
or so vehicles is approximately Normal with mean $18.7$ miles per gallon (mpg) and standard deviation $4.3$ mpg.
In my Chevrolet $(2.2)$ The $2008$ Chevrolet Malibu with a four-cylinder engine has a combined gas
mileage of $25 m p g$ . What percent of all vehicles have worse gas mileage than the Malibu?

Short Answer

Expert verified

$92.9 %$ of vehicles which have worse gas mileage than Malibu.

Step by step solution

Given information

The mean gas mileage, $渭 = 18.7 m p g$

The standard deviation of gas mileage, $蟽 = 4.3 m p g$

Chevrolet Malibu has a combined gas mileage of $25 m p g$

Concept

A regression line is a straight line that depicts the change in a response variable $y$ when an explanatory variable $x$ changes. By putting this $x$ into the equation of the line, you may use a regression line to predict the value of $y$ for any value of $x$

Calculation

We are provided that if the random variable $X$ denotes the number of vehicles with gas mileage. $X ~ N (渭, 蟽^{2})$ Where $渭 = 18.7 m p g$ and $蟽 = 4.3 m p g$

The Chevrolet Malibu gets $25$ miles per gallon on the highway and in the city. You must now determine what percentage of automobiles get worse gas mileage than the Malibu. To put it another way, we're meant to figure out P (X < 25)

$P (X < 25) = P (\frac{X 鈭� 渭}{蟽} < \frac{25 鈭� 18.7}{4.3}) = P (Z < 1.47) = 0.9286$