Chapter 3.2, Problem 79E

To determine

To find: the percent of vehicles having worse gas mileage than the Malibu

Answer to Problem 79E

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

Explanation of Solution

Given:

The mean gas mileage, $\mu =18.7\text{mpg}$

The standard deviation of gas mileage, $\sigma =4.3\text{mpg}$

Chevrolet Malibu has a combined gas mileage of 25 mpg.

Calculation:

If the random variable X denotes the number of vehicles that have gas mileage, then we are given that

  $X\sim N\left(\mu ,{\sigma }^2\right)$ Where $\mu =18.7$ mpg and $\sigma =4.3$ mpg

It is given that Chevrolet Malibu has a combined gas mileage of 25 mpg.

Now it is supposed to find the percent of vehicles that have worse gas mileage than the Malibu. In other words, we are supposed to calculate $P\left(X<25\right)$

  $\begin{array}{l}P\left(X<25\right)=P\left(\frac{X-\mu }{\sigma }<\frac{25-18.7}{4.3}\right)\\ =P\left(Z<1.47\right)\\ =0.9286\left(\text{From normal tables}\right)\end{array}$

Conclusion: Hence, there exist 92.9% of vehicles which have worse gas mileage than Malibu.