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 84 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 78 mg/mi and standard deviation 6 mg/mi.

(a) What is the probability that a single car of this model emits more than 84 mg/mi of NOX + NMOG? (Enter your answer rounded to four decimal places.)

(b) A company has 36 cars of this model in its fleet. What is the probability that the average NOX + NMOG level ?¯ of these cars is above 84 mg/mi? (Enter your answer rounded to four decimal places.)

Answer 1

Solution :

Given that ,

mean = = 78

standard deviation = = 6

a) P(x > 84) = 1 - p( x< 84)

=1- p P[(x - ) / < (84 - 78) / 6 ]

=1- P(z < 1.00)

Using z table,

= 1 - 0.8413

= 0.1587

b) n = 36

= = 78

= / n = 6 / 36 = 1

P( > 84) = 1 - P( < 84)

= 1 - P[( - ) / < (84 - 78) / 1]

= 1 - P(z < 6.00)

Using z table,    

= 1 - 1

= 0