>And you knew, eh?
Uh ... no. As far as I knew, there was no such formula.
However I googled and found a neat approximation due to Bagby.
Bagby, R. J. "Calculating Normal Probabilities." Amer. Math. Monthly 102, 4649, 1995
It looks like this:
>And is it any good ... Bagby's approximation?
It's excellent ... as indicated in Figure 2.
In Excel, you can use:
=0.5+IF(x>Mean,1,1)*0.5*SQRT(1(7*EXP(0.5*z*z)+16*EXP((2SQRT(2))*z*z)+EXP(z*z)*(7+0.25*PI()*z^2))/30)
where z = (x  Mean) / StandardDeviation
>How about a lognormal distribution?
For a Lognormal distribution, the logarithm of the variable has a Normal distribution.
So we need only change z, above, to:
where z = (LN(x)  Mean) / StandardDeviation
where Mean and StandardDeviation are the Mean and SD of the logarithm of x
... and x is a variable greater than 1 (example: x = 1 + StockReturn).
>The natural logarithm, eh?
Yes ... that's LN(x).
