Making auto parts A grinding machine in an auto parts plant prepares axles with a target diameter m = 40.125 millimeters (mm). The machine has some variability, so the standard deviation of the diameters is s = 0.002 mm. The machine operator inspects a random sample of 4 axles each hour for quality control purposes and records the sample mean diameter x . Assuming that the process is working properly, what are the mean and standard deviation of the sampling distribution of x ? Explain.

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The given data is:

By definition, the mean of the sampling distribution of is given as follows: