Poission distribution using Chebyshey's inequality

Question

Let $X$ have a Poisson distribution with $\mu = 100$. Use Chebyshev's inequality to determine a lower bound for $\Bbb{P}(75 < X < 125)$.

Amr · Answer 1 · 2012-11-10 12:15:02Z

up vote 0 down vote

The mean of X is 100 and the standard deviation of X is 10.

$P(|X-100|<2.5(10))=>1-1/2.5^2=0.84$

edited Nov 10 '12 at 12:15

answered Nov 7 '12 at 11:07

Amr
8,78821049

P(75<X<125)=P(|X-100|<2.5(10)) – Amr Nov 7 '12 at 11:09

Can you explain how? – user48495 Nov 7 '12 at 14:15

1

The variance is $10$? – Dilip Sarwate Nov 7 '12 at 15:26

Sorry, I meant the standard deviation. I will edit my ansewr. – Amr Nov 10 '12 at 12:14

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