In 2017, the entire fleet of light‑duty vehicles sold in theUnited States by each manufacturer must emit an average of no morethan 86 milligrams per mile (mg/mi) of nitrogen oxides (NOX) andnonmethane organic gas (NMOG) over the useful life (150,000 milesof driving) of the vehicle. NOX + NMOG emissions over the usefullife for one car model vary Normally with mean 82 mg/mi andstandard deviation 5 mg/mi.
(a) What is the probability that a single car of this modelemits more than 86 mg/mi of NOX + NMOG? (Enter your answer roundedto four decimal places.)
(b) A company has 25 cars of this model in its fleet. What isthe probability that the average NOX + NMOG level x¯ of these carsis above 86 mg/mi? (Enter your answer rounded to four decimalplaces.
