Question

The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000 miles of driving) of cars of a particular model varies Normally with mean 90 mg/mi and standard deviation 4 mg/mi. A company has 25 cars of this model in its fleet. Using Table A, find the level L such that the probability that the average NOX +NMOG level for the fleet greater than L is only 0.02? (Enter your answer rounded to three decimal places. If you are using Crunchlt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

Answer 1

By Central limit theorem, the average NOX + NMOG level will follow normal distribution with mean = 90 mg / mi and standard deviation = 4 / = 0.8 mg/mi

We need to find L , such that,

P( > L) = 0.02

=> P[Z > (L - 90) / 0.8] = 0.02

From Z distribution table, P(Z > z] = 0.02 => z = 2.054

So,

(L - 90) / 0.8 = 2.054

=> L = 90 + 0.8 * 2.054 = 91.6432

L = 91.643