Question

The level of nitrogen oxides (NOX) in the exhaust after 50,000 miles or fewer of driving of cars of a particular model varies Normally with mean 0.02 g/mi and standard deviation 0.01 g/mi. A company has 81 cars of this model in its fleet. What is the level L such that the probability that the average NOX level x for the fleet is greater than L is only 0.01? (Hint: This requires a backward Normal calculation. Round your answer to three decimal places.)

Answer 1

Answer:

For a level of 0.0174 or more of nitrogen oxide, the probability of fleet is 0.01.              

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 0.02 g/mi

Standard Deviation, σ = 0.01 g/mi

Sample size, n = 81

We are given that the distribution of  level of nitrogen oxides is a bell shaped distribution that is a normal distribution.

Standard error due to sampling:

$=\dfrac{\sigma}{\sqrt{n}} = \dfrac{0.01}{\sqrt{81}} = 0.0011$

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find the value of x such that the probability is 0.01

P(X > x)  

$P( X > x) = P( z > \displaystyle\frac{x - 0.02}{0.0011})=0.01$  

$= 1 -P( z \leq \displaystyle\frac{x - 0.02}{0.0011})=0.01$  

$=P( z \leq \displaystyle\frac{x - 0.02}{0.0011})=0.99$  

Calculation the value from standard normal z table, we have,  

$\displaystyle\frac{x - 0.02}{0.0011} = -2.326\\\\x = 0.0174$

For a level of 0.0174 or more of nitrogen oxide, the probability of fleet is 0.01.