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 70th 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

(a)

Let P₇₀ be the 70th Percentile

We are given :

We have,

Using Standard normal tables or using Excel function "NORMSINV()" we have :

70^th percentile for NOX exhaust = 1.6598

(b)

Interquartile range = Q₃ - Q₁

Q₃ = Third quartile

We have,

Using Standard normal tables or using Excel function "NORMSINV()" we have :

Now,

Q₁ = First quartile

We have,

Using Standard normal tables or using Excel function "NORMSINV()" we have :

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