(15.32) The level of nitrogen oxides (NOX) in the exhaust of cars of a particula

Question

(15.32) The level of nitrogen oxides (NOX) in the exhaust of cars of a particular model varies Normally with mean 0.22 grams per mile (g/mi) and standard deviation 0.053 g/mi. Government regulations call for NOX emissions no higher than 0.31 g/mi.

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

A company has 25 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 0.31 g/mi limit?

Explanation / Answer

mean = 0.22

standard deviation = 0.053

1)

probability (±0.001) that a single car of this model fails to meet the NOX requirement = P(X<0.31)

z value for 0.31 is (0.31-0.22)/0.053 = 1.69811

p value for z= 1.69811 using z table is 0.955256

probability (±0.001) that a single car of this model fails to meet the NOX requirement is 0.955256

2)

standard deviation of sample mean= 0.053/25 = 0.053/5 = 0.0106

z value for 0.31 is (0.31-0.22)/0.0106 = 8.49

p value for z= 8.49 using z table ~1

probability (±0.001) that the average NOX level x x of these cars is above the 0.31 g/mi limit is 1

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