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 92 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 88 mg/mi and standard deviation 4 mg/mi.

(a) What is the probability that a single car of this model emits more than 92 mg/mi of NOX ++ NMOG? (Enter your answer rounded to four decimal places.)

Probability - ?

(b) A company has 16 cars of this model in its fleet. What is the probability that the average NOX ++ NMOG level ?¯x¯ of these cars is above 92 mg/mi? (Enter your answer rounded to four decimal places.)

Probability - ?

Answer 1

for normal distribution z score =(X-μ)/σ
here mean=       μ=	88
std deviation   =σ=	4

a) probability that a single car of this model emits more than 92 mg/mi:

probability =

P(X>92)

=

P(Z>1)=

1-P(Z<1)=

1-0.8413=

0.1587

b)

sample size       =n=	16
std error=σx̅=σ/√n=	1.0000

  probability that the average NOX ++ NMOG level ?¯x¯ of these cars is above 92 mg/mi:

probability =

P(X>92)

=

P(Z>4)=

1-P(Z<4)=

1-1=

0.0000