[BigBiceps]

I am too lazy to compute your intervals (I actuallly would have to look up how to do it, because I forgot). Anyhow, here is a basic summary:

n = 2000 (sets of 100 hands)
m = 1.6 (mean big bets won per 100 hands)
s = 15.6 (standard devitions in big bets per 100 hands)

95% CI = m +/- 1.96 (s/sqrt(n))

So 95% of the time your next sample set of hands will be between [0.91 - 2.28] big blinds per hour.

You can easily infer that the chance you will be >3 or <0.5 will be less than 2% each.

All of this is of course assuming that you are playing the same, your opponents are playing the same, and any and all other underlying conditions have not changed.