document.write( "Question 717757: The average number of calories in a regular-size bagel is 240. If the standard deviation is 38 calories, find the range in which at least 75% of the data will lie. Use Chebyshev's Theorem. \n" ); document.write( "

Algebra.Com's Answer #440504 by Positive_EV(69) $\"\"$ $\"About$

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Chebyshev's Theorem states that at least 1 - 1/k^2 of the observations will be within k standard deviations of the mean. We want the range that 75% of data lie in, so set this equal to 75%:
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\n" ); document.write( "\n" ); document.write( ".75 = 1 - 1/k^2
\n" ); document.write( "1/k^2 = .25
\n" ); document.write( "4 = k^2
\n" ); document.write( "k = 2
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\n" ); document.write( "\n" ); document.write( "Thus, it can be shown that at least 75% of the observations will lie between +/- 2 standard deviations from the mean. The range is (240 +/- 2*38) = 164 to 316 Calories. \n" ); document.write( "

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