The response time of a system, X, is a random variable with a mean of 20 seconds and a

variance of 20 seconds. What can be said about P[ 0 < X < 40 ] ?

variance of 20 seconds. What can be said about P[ 0 < X < 40 ] ?

variance of 20 seconds. What can be said about P[ 0 < X < 40 ] ?

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New Wilmington, PA

Use Chebyshev's inequality: If X is a random variable with expected value μ and non-zero variance σ^{2}, then for any real number k > 0, P(|X-µ|<k)≥1-σ^{2}/k^{2}.

With µ=20=σ^{2}=k you get

P(|X-20|<20) ≥ 1-20/20² = .95

P(0 < X < 40) ≥ .95

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