SOLUTION: 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. Accor

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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?
Answer by stanbon(75887) About Me  (Show Source):
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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?
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Note: 24/25 = 0.96
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Solve for "n"
(1+ (1/n)^2) >= 0.96
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(1/n)^2 <= 0.04
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(1/n) <= 0.2
n >= 1/0.2 = 5
Note: At least 96% of the data is within 5 standard deviations of the mean.
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Ans: 1.65+-5*0.12
Lower limit: 1.05mg
Upper limit: 2.25mg
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Cheers,
Stan H.