Question

The mean income of a group of sample observations is $500, and the standard deviation is $30. According to Chebyshev’s Theorem, at least what percent of the incomes will lie between $410 and $590?

Answer 1

Given that

Now for Chebyshev’s Theorem we need to find k such that

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Now

That is we need to find at least what percentages of data values lie within 3 standard deviations of mean according to Chebyshev’s Theorem. The required percenatges is

That is at least 88.9% percent of the incomes will lie between $410 and $590.