Probability Question

Suppose you have a (possibly biased) coin which has a probability p of
coming up heads and 1-p coming up tails. Further suppose that Player
A flips that coin n times, yielding x heads and n-x tails. How many
standard deviations away from the norm would A's result be?

I can compute that the probability of A's result P(A) is C(n,x)(p^x)(1-
p)^(n-x) and that the population standard deviation sigma is sqrt(np(1-
p)), and that these two equations will be important for the result.
However, it's not obvious where I go from here. I am essentially
looking for an equation of the form SD(p,n,x).

In a simple case where p=0.5 and n=16, P(A,x)=C(16,x)/2^16 and sigma =
2. Since x=8 is the expected value, SD(0.5,16,8) should be 0; if x=0
or x=16, I would expect SD(0.5,16,x) to be somewhere around 3 range,
since this is what I would guess how many sigma's away such a result
might be. Yet I do not see any obvious (or justifiable) way to yield
this result.

Any suggestions?
.

Relevant Pages

  • Re: Why the cards must have a memory
    ... Probability theory assumes uncertainty, ... This is why I used the "tiny universe" scenario, ... ***it assumes that the probability is heads half the time FROM NOW ... incident in this case being a coin toss). ...
    (rec.gambling.poker)
  • Re: WHY the cards have a memory
    ... If we keep flipping a coin over and ever, we expect that the ratio # of heads/# of tosses will approach 0.5. ... It never says if I flip a coin 10 times, it "must" come down heads 5 times. ... probability of exactly 5 heads and 5 tails is about .2461. ... As presently understood, the universe ...
    (rec.gambling.poker)
  • Re: Number Due
    ... If you flip a coin 100 times your math says you could toss 100 heads ... Your problem is that when you see 10 heads in a row (wth a fair coin) you're ... All of the calculations of probability theory are based on ...
    (rec.gambling.craps)
  • Re: WHY the cards have a memory
    ... assumption--- that if you flip a coin, ... up heads, half the time. ... It never says if I flip a coin 10 times, ... probability of exactly 5 heads and 5 tails is about .2461. ...
    (rec.gambling.poker)
  • Re: Krigman article about sevens due
    ... You are tossing a fair coin. ... The probability is .5 for heads and .5 for tails. ...
    (rec.gambling.craps)