Light vehicles sold in a country must emit an average of no more than 0.04 grams

Question

Light vehicles sold in a country must emit an average of no more than 0.04 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 0.02 g/mi and standard deviation 0.01 g/mi. (a) What is the probability that a single car of this model emits more than 0.04 g/mi of NOX? (Round your answer to four decimal places.) 02275 (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 0.04 g/mi? (Round your answer to four decimal places.)

Explanation / Answer

Solution:-

Light vehicles sold in a country must emit an average of no more than 0.04 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 0.02 g/mi and standard deviation 0.01 g/mi.

Z value for 0.04, z=(0.04 - 0.02) / 0.01 = 2

P( x >0.04) = P( z >2)

= 0.02275


(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 0.04 g/mi? (Round your answer to four decimal places.)

Standard error = 0.01/sqrt(25) =0.002

Z value for 0.04, z = (0.04 - 0.02)/0.002 = 10

P(mean x >0.04) = P( z >10)

< 0.00001

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