Approximate the probability of getting 500 heads out of a 1000 coin flip of unbiased coins to be within 5% of its true value (without the use of a calculator).
I know that an exact probability is $\binom{1000}{500}(.5)^{1000} = .02522...$
I am unsure how one could simplify this problem through estimation to get an approximate answer however.
Thanks for any help.