Question

5)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 20th 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

5)

Solution :

mean = = 1.45

standard deviation = = 0.40

Using standard normal table,

(a)

P(Z < z) = 20% = 0.20

P(Z < -0.8416) = 0.20

z = -0.8416

Using z-score formula,

x = z * +

x = -0.8416 * 0.40 + 1.45 = 1.1134

20th percentile = 1.3334

(b)

P(Z < z) = 75% = 0.75

P(Z < 0.6745) = 0.75

z = 0.6745

Using z-score formula,

x = z * +

x = 0.6745 * 0.40 + 1.45 = 1.7198

Q₃ = 75th percentile = 1.7198

P(Z < z) = 25% = 0.25

P(Z < -0.6745) = 0.25

z = -0.6745

Using z-score formula,

x = z * +

x = -0.6745 * 0.40 + 1.45 = 1.1802

Q₁ = 25th percentile = 1.1802

Interquartile range = IQR = Q₃ - Q₁ = 1.7198 - 1.1802 = 0.5396