Estimating BB/100

[indianaV8]

I have two questions.

If I want to find out BB/100h range, and I know the STD, I estimate the range boundaries (with given confidence level, e.g. for 95% z = 1.96) by the formula:
z*(STD/sqrt(N))
where N is the number of hands.

Now the questions are:

1) What if I don't know the STD? If I have played 20k hands, but I don't know what the STD is (and I calculate it from this 20k sample). Is the above formula still correct?

2) What if the distribution is not normal? Do one gets better results if the outcomes of each event are very limited, e.g. jam/fold case you either fold (ev=0), fold BB (ev = -BB), or you go allin (EV +- yourstack). Does this has anything to do in the above formula, or in the above formula the mean (BB/100) will follow normal distribution in any case?

Thanks

P.S. Any digestable links/references for are also appreciated ...