Winrate Confidence Interval, Can Someone Check My Math

[XChamp]

Here are the numbers. Over the past 12,490 hands I made $4,558 in 60.0 hours with a standard deviation of $163.8/100 hands.

I want to find the condidence that I make $50+/hr, so


u = 4,558

s = 163.8*sqrt(124.9) = 1830.61

if i make $50/hr then my expected winnings would be 60hrs*$45/hr = $2,700 over 60 hours. I say $45 because I average $5 back/hr from rakeback, which is independant of the quality of my play.

So to find the confidence that I make $50/hr or more by playing in this game I do the following calculation:

Integral[ 1/(s*SQRT(2*Pi)) * e^(-(x-u)^2/(2*s^2)), x, 2700, +infinity)

= 0.845

So what all this means is that if I found 100 people with the exact same stats as me (and they all averaged $5/hr from rakeback), about 85 of them would go on to make $50/hr or more playing in the same game.

Is this how I go about doing this? I haven't done something like this in a few months so I am rusty.

Thanks for the help

[XChamp]

Just to clarify, in the above post 's' is the standard deviation of the mean win total for 12,490 hands.