Thread: Empirical Rule & Chebyshev’s Theorem

Calculate the probability of a result falling within 2.5 standard deviations from the mean, using

a) Chebyshev’s Theorem

b) Empirical Rule

Please help
[/FONT]

I believe that you have not put enough information in the question like what is the mean all you told us was that its with in 2.5 of the mean.

chebs thm

P(M-OK< X < M+Ok)>= 1- 1/k^2

Originally Posted by Amy

Calculate the probability of a result falling within 2.5 standard deviations from the mean, using

a) Chebyshev’s Theorem

b) Empirical Rule

Please help
[/font]

a) Chebyshev's inequality tells us that:

P(|x-mu|>= k sigma) <= 1/k^2

so P(|x-mu|) >= 2.5 sigma) <= 1/2.5^2 = 0.16

So P(|x-mu| < 2.5 sigma) = 1-0.16 = 0.84.

b) here I presume that we are to assume normality, so we look 2.5 up
in a table of the standard normal distribution to get:

So P(|x-mu| < 2.5 sigma) = 0.9876.

RonL