A process that manufactures steel bolts is supposed to be calibrated to produce bolts with a mean length of \(5 \mathrm{~cm}\). A sample of 100 bolts has a mean length of \(5.02 \mathrm{~cm}\). The population standard deviation is \(0.06 \mathrm{~cm}\). Let \(\mu\) be the mean length of bolts manufactured by this process.

a. Find the \(P\)-value for testing \(H_{0}: \mu=5\) versus \(H_{1}: \mu eq 5\).

b. Do you believe it is plausible that the process is properly calibrated, or are you convinced that it is out of calibration? Explain.