A grinding machine in an auto parts plant prepares axles with a target diameter = 40.125 millimeters (mm). The machine has some variability, so the standard deviation of the diameters is = 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.

Only R should be used for any plots or calculations.