Howdy! I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we're going to learn how to use Chebyshev's Theorem to derive proportions. Here's our problem statement: Using the accompanying table of data, a blood platelet counts of women have a bell-shaped distribution with a mean of 255.0 and a standard deviation of 65.3. (All units are thousand cells per microliter.) Using Chebyshev's Theorem, what is known about the percentage of women with platelet counts that are within three standard deviations of the mean? What are the minimum and maximum possible platelet counts that are within three standard deviations of the mean?
OK, the first part asks for Chebyshev's Theorem, and we want to know, you know, what percentage of the data are within three standard deviations of the mean. Well, Chebyshev's Theorem — it's just basically tabulated data. It comes from an equation that he derived, but you don't have to use the equation. You just have to just take it straight off the table. So you want the value for within three standard deviations. Well, just take it straight off the table. We're supposed to round to the nearest integer. Well done!
Now, the second part asks, “What are the minimum and maximum possible platelet counts that are within three standard deviations of the mean?” Well, they give us values for the mean and the standard deviation here in the problem statement. So all I need to do now is whip out my calculator and punch that out. So the minimum is going to be the mean minus three standard deviations. So I'm going to go ahead and calculate that here. And then to get the maximum, I'm going to do the same thing, only instead of subtracting, now I have to add. Well done!
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