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 ] ?

Tutors, please sign in to answer this question.

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

- Probability & Statistics 737
- Statistics 1336
- Finite Mathematics 581
- Math 9892
- Probability Problems 240
- Random Variable 16
- Math Help 5461
- Math Help For College 1400
- Venn Diagram 104
- Sets 154