Question

In its Fuel Economy Guide for 2016 model vehicles, the Environmental Protection Agency gives data on 1170 vehicles. There are a number of high outliers, mainly hybrid gas-electric vehicles. If we ignore the vehicles identified as outliers, however, the combined city and highway gas mileage of the other 1146 vehicles is approximately Normal with mean 23.0 miles per gallon (mpg) and standard deviation 4.9 mpg. The 2016 Volkswagen Beetle with a four-cylinder 1.8-L engine and automatic transmission has combined gas mileage of 28 mpg. Find the percentage of 2016 vehicles that have better gas mileage than the Beetle's gas mileage.(Enter your answer rounded to two decimal places.) percentage: __.

Answer 1

15.386% of the 2016 card will have better gas mileage than the 2016 beetle.

Explanation:

Hello!

The study variable is:

X: combined gas mileage of city and highway of a 2016 vehicle.

X~N(μ;σ²)

μ= 23.0 mpg

σ= 4.9 mpg

The 2016 Volkswagen Beetle has a combined has a mileage of 28 mpg and you need to find what percentage of 2016 vehicles have a better gas mileage than the Bettle's, symbolically:

P(X > 28)

Since the variable has a normal distribution you can use the standard normal to find out the asked percentage:

P(Z >
`(28 - 23)/(4.9)`) = P(Z > 1,02) =

1 - P(Z ≤ 1.02)= 1 - 0.84614 = 0.15386

15.386% of the 2016 card will have better gas mileage than the 2016 beetle.

I hope it helps!