Question

The level of nitrogen oxides (NOX) in the exhaust of cars of a particular model varies Normally with mean 0.21 grams per mile (g/mi) and standard deviation 0.051 g/mi. Government regulations call for NOX emissions no higher than 0.29 g/mi. What is the probability (±0.001) that a single car of this model fails to meet the NOX requirement? A company has 12 cars of this model in its fleet. What is the probability (±0.001) that the average NOX level x⎯⎯⎯ x ¯ of these cars is above the 0.29 g/mi limit?

Answer 1

(a)

Question:

What is the probability (±0.001) that a single car of this model fails to meet the NOX requirement?

= 0.21

= 0.051

To find: P(X > 0.29):

Z = (0.29 - 0.21)/0.051

= 1.5686

By Technology, Cumulative Area Under Standard Normal Curve = 0.9416

So,

P(X > 0.29)= 1 - 0.9416 = 0.0584

So,

Answer is:

0.0584

(b)

Question:

What is the probability (±0.001) that the average NOX level of these cars is above the 0.29 g/mi limit?

= 0.21

= 0.051

n = 12

SE = /

= 0.051/

= 0.0147

To find: P( > 0.29):

Z = (0.29 - 0.21)/0.0147

= 5.4339

By Technology, Cumulative Area Under Standard Normal Curve = 0.99999997

So,

P( > 0.29)= 1 - 0.99999997= 0.00000003

So,

Answer is:

0.000