Exercise · ZW-CHEBYSHEV-INEQUALITY-008 · ★★☆ Intermediate
What is the smallest \(k\) for which Chebyshev guarantees \(P(|X-\mu|\ge k\sigma)\le0.04\)?
Choose one option.
Show answer
- D. \(5\)
Explanation
We need \(1/k^2\le0.04=1/25\), i.e. \(k\ge5\). The 25 would be \(k^2\).
Review the concept: Chebyshev inequality
Chebyshev's inequality bounds the probability \(P\) that a variable \(X\) deviates from its mean \(\mu\) by more than \(k\) standard deviations \(\sigma\), using only its variance.
\[P\big(|X-\mu|\ge k\sigma\big)\le\dfrac{1}{k^2}\]
More practice problems: chebyshev inequality
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