Question

The Environmental Protection Agency (EPA) requires that the exhaust of each model of motor vehicle be tested for the level of several pollutants. The level of oxides of nitrogen (NOX) in the exhaust of one light truck model was found to vary among individual trucks according to an approximately Normal distribution with mean $\mu =1.45$ grams per mile driven and standard deviation $\sigma =0.40$ gram per mile. Which of the following best estimates the proportion of light trucks of this model with $NOX$ levels greater than $2$ grams per mile?

$$\begin{gathered} a.0.0228 \\ b.0.0846 \\ c.0.4256 \\ d.0.9154 \\ e.0.9772 \end{gathered}$$

Short answer

The correct option is (b) 0.0846

Step-by-step solution

Given information

$$\begin{gathered} \mu =1.45 \\ \sigma =0.40 \\ x=2 \end{gathered}$$

Concept

$z=\frac{x-\mu }{\sigma }$

Calculation

$$\begin{gathered} z=\frac{x-\mu }{\sigma } \\ =\frac{2-1.45}{0.40} \\ =1.375 \end{gathered}$$

$$\begin{gathered} P(x>2)=P(z>1.375) \\ =1-P(z<1.375) \\ =1-0.91545 \\ =0.08455 \end{gathered}$$

As a result, $0.0846$ of this model's light trucks had a $NOX$ level greater than $2$ grams per mile.

Hence, the correct option is (b)