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If a weighted coin is tossed N times, count the times it lands heads as H.
The probability of landing heads is P(H).
I assume the expected value of H is N*P(H).
But how do I find out what range of H is X% likely to happen? For example,
I want to be able to say that in 90% of cases H will be in the range (A,B).
What I've done so far is for 0<=H<=N calculated (N choose H)/P, where P is
the total permutations of N items in N. This should give me the probability
of exactly H heads coming up, yes? I can keep a cumulative total of these
probabilites for each H, and then figure out the range of H between (say)
10% and 90%. But it seems a bit long-winded, I can't figure out how to
calculate the range directly. Also Excel can't figure out the permutations
when N is bigger than 150 or so, I want it to work for higher values of N.
Any ideas? Hopefully it's something obvious!
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