Let S be the number of heads in 1,000,000 tosses of a fair coin. How does on use (a) Chebyshev's inequality and (b) the Central Limit Theorem to estimate the probability that S lies between 499,500 and 500,500?

Thanks so much!!!

Printable View

- Aug 2nd 2009, 08:08 PMmorganforChebyshev and Central Limit Theorem
Let S be the number of heads in 1,000,000 tosses of a fair coin. How does on use (a) Chebyshev's inequality and (b) the Central Limit Theorem to estimate the probability that S lies between 499,500 and 500,500?

Thanks so much!!! - Aug 2nd 2009, 08:17 PMmatheagle
n=1,000,000 and p=.5 approximating this binomial with a normal (CLT) you need

and

Since you want the probability of an event that has at its center this is straightforward.

As for cheby's figure out your k at http://en.wikipedia.org/wiki/Chebyshev's_inequality

look under Probabilistic statement - Aug 4th 2009, 03:12 PMmorganfor
I'm just confused because for this problem doesn't k=1 for Chebyshev so that 1/k^2 = 1 which means that there is a 0 probability that S lies between 499,500 and 500,500?