The level of nitrogen oxides (NOX) in the exhaust of cars of a particular model varies Normally with mean 0.25 grams per mile (g/mi) and standard deviation 0.08 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 36 cars of this model in its fleet. What is the probability that the average NOX level of these cars is above the 0.31 g/mi limit? (Use 3 decimal places)
(c) What average NOX level for the fleet is less than 0.01 of all other average NOX levels? Hint: this requires a backward Normal calculation. (Use 2 decimal places)