Question

The Environmental Protection agency 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 individually trucks according to a Normal distribution with mean 1.45 grams per mile driven and standard deviation 0.40 grams per mile.

(a) What is the 30th percentile for NOX exhaust, rounded to four decimal places?

(b) Find the interquartile range for the distribution of NOX levels in the exhaust of trucks rounded to four decimal places.

Answer 1

Here,

X ~ Normal(1.45, 0.4²)

a)

The 30th percentile for NOX exhaust is 1.2402

b) To find the first quartile (Q₁),

To find the third quartile (Q₃),

The first quartile (Q₁) is 1.1802

The third quartile (Q₃) is 1.7198

The interquartile range for the distribution of NOX levels in the exhaust of trucks is = Q₃ - Q₁ = 1.7198 - 1.1802 = 0.5396