Question

The level of nitrogen oxides (NOX) in the exhaust of a particular car model varies with mean 0.8 grams per mile and standard deviation 0.17 grams per mile . (a) What sample size is needed so that the standard deviation of the sampling distribution is 0.01 grams per mile

Answer 1

Answer:

Sample size, n = 289

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 0.8 grams per mile

Standard Deviation, σ = 0.17 grams per mile

We have to find the sample size such that standard deviation of the sampling distribution is 0.01 grams per mile.

Formula:

Standard error =

$\dfrac{\sigma}{\sqrt{n}}$

Putting values, we get,

$\dfrac{\sigma}{\sqrt{n}} = 0.01\\\\\dfrac{0.17}{\sqrt{n}} = 0.01\\\\\sqrt{n} = \dfrac{0.17}{0.01}\\\sqrt{n} = 17\\\Righatrrow n = 289$

Thus, the sample size must be 289 so that the sampling distribution have a standard deviation of 0.01 grams per mile.