Question

54. Making auto parts A grinding machine in an auto parts plant prepares axles with a target diameter μ 40.125 millimeters (mm). The machine has some variability, so the standard deviation of the diameters is σ = 0.002 mm. The machine operator inspects a random sample of 4 axles each hour for quality contro purposes and records the sample mean diameter Assume the machine is working properly. a) Identify the mean of the sampling distribution of b Calculate and interpret the standard deviation of the sampling distribution ofx·Verify that the 10% condi- tion is met

Answer 1

a) Since the sample is taken from a large population hence it follows central limit theorem, which states that the sample mean is approximately equal to the population mean.

Hence $\bar{X}= \mu=40.125$

b) Again by central limit theorem the standard deviation of the sample is calculated as

$S=\frac{\sigma}{\sqrt{n}}$

Since n=4 hence

S=0.001.

The law of 10 % state that the sample proportion should not be more than 0.10 of population.

Here the sample size is very small in compared to population and also we will be using t distribution because n<<30.

So the condition for 10 % is satisfied here.