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.)

Accepted Solution

Answer:a. 19.68 miles per gallon.b. 26.32 miles per gallon.Step-by-step explanation:Mean gas mileage (μ) = 23.0 mpgStandard deviation (σ) = 4.9 mpg In a normal distribution, for any length X, the z-score is determined by the following expression:  [tex]z=\frac{X-\mu}{\sigma}[/tex]In a normal distribution, the 25th percentile  (first quartile) of a normal distribution has a corresponding z-score of z = -0.677 and the 75th percentile  has a corresponding z-score of z = 0.677 a. The first quartile of the distribution of gas mileage is[tex]-0.677=\frac{X_{25}-23}{4.9}\\X_{25}=19.68\ mpg[/tex]19.68 miles per gallon.b. The third quartile of the distribution of gas mileage is[tex]0.677=\frac{X_{25}-23}{4.9}\\X_{25}=26.32\ mpg[/tex]26.32 miles per gallon.