Question: A grinding machine for auto axles. An automatic grinding machine in an auto parts plant prepares axles with a target diameter \(\mu=40.135\) millimeters \((\mathrm{mm})\). The machine has some variability, so the standard deviation of the diameters is \(\sigma=0.003 \mathrm{~mm} .\) A sample of 4 axles is inspected each hour for process control purposes, and records are kept of the sample mean diameter. If the process mean is exactly equal to the target value, what will be the mean and standard deviation of the numbers recorded?

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