Question

The level of nitrogen oxides (NO x ) in the exhaust of cars of a particular model varies Normally, with mean 0.25 gram per mile (g/mi) and standard deviation 0.05 g/mi. Government regulations call for NO x emissions no greater than 0.3 g/mi. A company has four cars of this model in its fleet. What is the probability that the average NO x level of these cars is above the 0.3 g/mi limit?

Answer 1

Probability that the average NO x level of these cars is above the 0.3 g/mi limit is 0.15866.

Explanation:

We are given that the level of nitrogen oxides (NO x ) in the exhaust of cars of a particular model varies Normally, with mean 0.25 gram per mile (g/mi) and standard deviation 0.05 g/mi.

Let X = level of nitrogen oxides (NO x ) in the exhaust of cars

So, X ~ N(
`\mu=0.25,\sigma^(2)=0.05^(2)`)

Now, the z score probability distribution is given by;

Z =
`(X-\mu)/(\sigma)` ~ N(0,1)

where,
`\mu` = population mean

`\sigma` = standard deviation

So, probability that the average NO x level of these cars is above the 0.3 g/mi limit is given by = P(X > 0.30 g/mi)

P(X > 0.30) = P(
`(X-\mu)/(\sigma)` >
`(0.30-0.25)/(0.05)` ) = P(Z > 1) = 1 - P(Z
`\leq` 1)

= 1 - 0.84134 = 0.15866

Therefore, probability that the average NO x level of these cars is above the 0.3 g/mi limit is 0.15866.

Answer 2

0.1587 is the probability that the average nitrogen oxides level of cars is above the 0.3 g/mi limit.

Explanation:

We are given the following information in the question:

Mean, μ = 0.25 gram per mile

Standard Deviation, σ = 0.05 g/m

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

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

P(score greater than 0.3)

P(x > 0.3)

`P( x > 0.3) = P( z > \displaystyle(0.3 - 0.25)/(0.05)) = P(z > 1)`

`= 1 - P(z \leq 1)`

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

`P(x > 0.3) = 1 - 0.8413 = 0.1587 = 15.87\%`

0.1587 is the probability that the average nitrogen oxides level of cars is above the 0.3 g/mi limit.