Question

The level of nitrogen oxides (NOX) in the exhaust of cars of a particular model varies Nor- mally with mean 0.2 grams per mile (g/mi) and standard deviation 0.05 g/mi. Government regulations call for NOX emissions no higher than 0.3 g/mi.

a.What is the probability that a single car of this model fails to meet the NOX requirement

b. company has 25 cars of this model in its fleet. What is the probability that the average NOX level x of these cars is above the 0.3 g/mi limit?

Answer 1

u = 0.2, = 0.05

z = (x-u)/

a) probability that a single car of this model fails to meet the NOX requirement

=> P(x > 3)

= P(z > (0.3-0.2)/0.05)

= P(z > 2)

= 0.0228

b. company has 25 cars of this model in its fleet. What is the probability that the average NOX level x of these cars is above the 0.3 g/mi limit?

= P(z > (0.3-0.2)/0.05) (as standard deviation is for population we wont divide by sample size)

= P(z > 2)

= 0.0228