SOLUTION: A study of the nicotine contents of a certain brand of cigarette shows that on the
average one cigarette contains 1.52mg of nicotine with a standard deviation of
0.07mg. Accordin
Algebra.Com
Question 1200797: A study of the nicotine contents of a certain brand of cigarette shows that on the
average one cigarette contains 1.52mg of nicotine with a standard deviation of
0.07mg. According to Chebyshev’s theorem, between what values must the
nicotine content be for at least 48/49 of all cigarettes of this brand?
Answer by GingerAle(43) (Show Source): You can put this solution on YOUR website!
**1. Understand Chebyshev's Theorem**
* Chebyshev's Theorem states that for any data set (regardless of its distribution), at least 1 - (1/k²) of the data values will fall within k standard deviations of the mean.
**2. Determine the k value**
* We are given that at least 48/49 of the cigarettes fall within the desired range.
* Therefore, 1 - (1/k²) = 48/49
* Solving for k:
* 1/k² = 1 - 48/49 = 1/49
* k² = 49
* k = 7
**3. Calculate the lower and upper bounds**
* Lower bound: Mean - k * Standard Deviation = 1.52 - 7 * 0.07 = 1.52 - 0.49 = 1.03 mg
* Upper bound: Mean + k * Standard Deviation = 1.52 + 7 * 0.07 = 1.52 + 0.49 = 2.01 mg
**Conclusion**
According to Chebyshev's Theorem, at least 48/49 of the cigarettes of this brand must have nicotine content between **1.03 mg and 2.01 mg**.
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