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The mean gas mileage,$\mathrm{μ}=18.7mpg$

The standard deviation of gas mileage,$\mathrm{σ}=4.3mpg$

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 $x$

We are provided that if the random variable $X$ denotes the number of vehicles with gas mileage $X~N(\mathrm{μ},{\mathrm{σ}}^2)$

Where $\mathrm{μ}=18.7mpg$and $\mathrm{σ}=4.3mpg$

Its goal is to find the vehicle with the best gas mileage among the top $10\%$of all automobiles.

To put it another way, find the $z$' that corresponds to the top $10\%$of the population.

That is, $$\begin{gathered} P(z>z^1)=10\% \\ ⇒P(z>z^1)=0.90 \end{gathered}$$

From standard normal tables, the value of $z$ corresponding to $0.90$cumulative area is $1.28$

That is, $$\begin{gathered} z^1=1.28 \\ ⇒\frac{x−\mathrm{μ}}{\mathrm{σ}}=1.28 \\ ⇒x=18.7+1.28×4.3 \\ =24.204 \end{gathered}$$

As a result, the highest gas mileage that falls into the top $10\%$of all vehicles is $24.204mpg$