Chebyshev Theorem: Probability of Parts Within .006 of Mean

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Over the range of cylindrical parts manufactured on a computer-controlled lathe, the standard deviation of the diameters is .002 millimeter.

(a) What does Chebyshev's theorem tell us about the probability that a new part will be within .006 units of the mean 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?

I know the answer for (a) the probability is at least 8/9 but I'm not sure about (b). I'm thinking isn't the proportion 8/9 as well, about 356 out of 400 will lie in that interval.
 
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