Over the range of cylindrical parts manufactured on a computer-controlled lathe, the standard deviation of the diameters is 0.002 millimeter.

(a) What does Chebyshev's theorem tell us about the probability that a new part will be within 0.006 unit of the mean \(\mu\) for that run?

(b) If the 400 parts are made during the run, about what proportion do you expect will lie in the interval in part (a)?