In 2017, the entire fleet of light‑duty vehicles sold in the United States by each manufacturer must emit an average of no more than 91 milligrams per mile (mg/mi) of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) over the useful life (150,000 miles of driving) of the vehicle. NOX + NMOG emissions over the useful life for one car model vary Normally with mean 86 mg/mi and standard deviation 5 mg/mi.
What is the probability that a single car of this model emits more than 91 mg/mi of NOX + NMOG? Give your answer to four decimal places.
A company has 36 cars of this model in its fleet. What is the probability that the average NOX + NMOG level x¯ of these cars is above 91 mg/mi? Give your answer to four decimal places.
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