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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 0.09 g/mi. Government regulations call for NOX emissions no higher than 0.31 g/mi.

(a) What is the probability that a single car of this model fails to meet the NOX requirement? (Use 3 decimal places.)

(b) A company has 81 cars of this model in its fleet. What is the probability that the average NOX level x of these cars is above the 0.31 g/mi limit? (Use 3 decimal places.)

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