The level of nitrogen oxides (NO_x) in the exhaust of cars of a particular model varies Normally, with mean 0.25 gram per mile (g/mi) and standard deviation 0.05 g/mi. Government regulations call for NO_x emissions no higher than 0.3 g/mi. A company has four cars of this model in its fleet. What is the probability that the average NO_x level of these cars is above the 0.3 g/mi limit?

Question

Quizplus · Accepted Answer

The average NO_x level of these four cars follows a Normal distribution with mean μ = 0.25 and standard deviation σ/√(n) = 0.05/√(4) = 0.025. To find the probability that the average NO_x level of these cars is above the limit of 0.3 g/mi, we need to find P(X > 0.3) for the Normal distribution with μ = 0.25 and σ/√(n) = 0.025. Using standard Normal distribution tables or a calculator, we find P(Z > (0.3-0.25)/0.025) = P(Z > 2) = 0.0228. Thus, the probability that the average NO_x level of these cars is above the 0.3 g/mi limit is 0.0228 or 2.28%, which is closest to choice (D).

The Level of Nitrogen Oxides (NOx) in the Exhaust of Cars

The Level of Nitrogen Oxides (NO_x) in the Exhaust of Cars