Question

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 86 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 80 mg/mi and standard deviation 4 mg/mi. (a) What is the probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG? (Enter your answer rounded to four decimal places.)

Answer 1

probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG = 0.8668

Explanation:

mean, μ = 80 mg/mi

Standard deviation,
`\sigma = 4 mg/mi`

probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG

`P(X > x ) = P(z > (x - \mu)/(\sigma))`

`P(X > x ) =1 - P(z < (x - \mu)/(\sigma))`

`P(X > 86 ) =1 - P(z < (86 - 80)/(4))`

P(X > 86) = 1 - P(z < 1.5)

From the standard normal table, P(z < 1.5) = 0.9332

P(X > 86) = 1 - 0.9332

P(X > 86) = 0.0668