91影视

Given in the question that,

Mean $=40.125mm$

Standard deviation$=0.002mm$

Number of axles$=4$we have to find that how many axles would you need to sample if you wanted the standard deviation of the sampling distribution $\stackrel{炉}{x}$to be$0.0005$.

The mean of the sampling distribution of $\stackrel{铃�}{p}is{渭}_{\stackrel{铃�}{p}}=p$

The standard deviation of a sample distribution of the sample mean $\stackrel{炉}{x}$if the population standard deviation is can be written as,

${蟽}_{\stackrel{炉}{x}}=\frac{蟽}{\sqrt{n}}$

Here, number of axles is the sample size.

Also,

Population standard deviation,$蟽=0.002$

Standard deviation of the sample,${蟽}_{\stackrel{炉}{x}}=0.0005$

It is known that the standard deviation of a sample distribution of the sample mean if the population standard deviation is can be written as,

${蟽}_{\stackrel{炉}{x}}=\frac{蟽}{\sqrt{n}}$

To find the sample size, use the above formula.

Write the formula as:

$\sqrt{n}=\frac{蟽}{{蟽}_{\stackrel{炉}{x}}}$

squares both side

$n=\frac{{蟽}^2}{{蟽}_{\stackrel{炉}{x}}2}$

substitute $0.002for蟽and0.0005for{蟽}_{\stackrel{炉}{x}}$

$n=\frac{0.{002}^2}{0.{0005}^2}=16$

hence the required number of axles to sample is$16$