Probability... Pollutants in auto exhausts. Light vehicles sold in the United St

Question

Probability...

Pollutants in auto exhausts. Light vehicles sold in the United States must emit an average of no more than 0.05 grams per mile (g/mi) of nitrogen oxides (NOX) after 50,000 or fewer miles of driving. NOX emissions after 50,000 or fewer miles of driving for one car model vary Normally with mean 0.03 g/mi and standard deviation 0.01 g/mi. (a) What is the probability that a single car of this model emits more than 0.05 g/mi of NOX? (b) A 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 0.05 g/mi?

Explanation / Answer

a) here P(X>0.05)=1-P(X<0.05)=1-P(Z<(0.05-0.03)/0.01)=1-P(Z<2)=1-0.97725=0.02275

b) for n=25; std error =std deviaiton/(n)1/2 =0.002

P(X>0.05)=1-P(X<0.05)=1-P(Z<(0.05-0.03)/0.002)=1-P(Z<10)=1-1=0.0000

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