Thursday, August 20, 2015

Example of Chebyshev's inequality

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Chebyshev's inequality: P[|t-E(t)|<k] ≥ 1- Var(t)/k2
If k > 1, then at least (1-1/k2) 100% of the data lies between (μ-kσ, μ+kσ).
P[|t-E(t)|<3σ2] ≤ 1 - σ2/(9σ2) = 8/9
Example:
If,
μ = 60
σ = 15.8
(30,90)
The interval indicates the amount of time different women take to get ready for work.
Here, UL = Upper Limit = 90
k = (UL - μ)/ σ
= (90-60)/15.8
=1.8487
Now,
{1- 1/(1.8987)2}100% = 72.3 %
Comment:
72.3 % women take 30 to 90 minutes to get ready for work.
At most (100-72.3) % = 28%.

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