[AceKQJT]

Ok. So I'm gonna flip a coin 1000 times. I am looking for a range in which heads comes up with 90% certainty. I'll give an example, because I can't even understand what I've written:

I know that the chance of heads coming up exactly 500 times is 5.253%. I can calculate the binomial distribution for each case of "successes", then manually find that 90.6% of the time, heads will show up between 474 and 526. I could express this by saying

"If you flip a coin 1000 times, there is a 90.6% chance that the coin will come up heads 500 (+/- 26) times."

Is there any way to come to this result other than calculating individual successes for the entire trial, and then manually adding the results?

--Casey