Chebyshev Theorem: Probability of Parts Within .006 of Mean

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SUMMARY

Chebyshev's theorem indicates that for a set of cylindrical parts manufactured with a standard deviation of 0.002 millimeters, the probability that a new part will fall within 0.006 units of the mean is at least 8/9. Given a production run of 400 parts, it is expected that approximately 356 parts will lie within this interval, confirming the proportion of parts that meet this criterion aligns with the probability derived from Chebyshev's theorem.

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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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Yes, that is correct.
 

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