document.write( "Question 986311: A study of the nicotine contents of a certain brand of cigarette shows that on the average of one cigarette contains 1.65 mg of nicotine with a standard deviation of 0.12 mg. According to chebyshev's theorem, between what values must the nicotine content be for at least 24/25 of all cigarettes of this brand? \n" ); document.write( "

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A study of the nicotine contents of a certain brand of cigarette shows that on the average of one cigarette contains 1.65 mg of nicotine with a standard deviation of 0.12 mg. According to chebyshev's theorem, between what values must the nicotine content be for at least 24/25 of all cigarettes of this brand?
\n" ); document.write( "--------
\n" ); document.write( "Note: 24/25 = 0.96
\n" ); document.write( "------
\n" ); document.write( "Solve for \"n\"
\n" ); document.write( "(1+ (1/n)^2) >= 0.96
\n" ); document.write( "-----
\n" ); document.write( "(1/n)^2 <= 0.04
\n" ); document.write( "-----
\n" ); document.write( "(1/n) <= 0.2
\n" ); document.write( "n >= 1/0.2 = 5
\n" ); document.write( "Note: At least 96% of the data is within 5 standard deviations of the mean.
\n" ); document.write( "----------
\n" ); document.write( "Ans: 1.65+-5*0.12
\n" ); document.write( "Lower limit: 1.05mg
\n" ); document.write( "Upper limit: 2.25mg
\n" ); document.write( "----------------
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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