Confidence Interval for 1-Table Tournament ROI

[TomCollins]

Correct me if I'm wrong. I think I'm doing this correctly.

Suppose I have 70 tournaments (10 players) with 15 1sts, 5 2nds, and 13 3rds. The payouts on each of those is $195, $95, and $45. This means I also have 37 values of -$55.

So I take the S.D. of these 70 values and get $100.68

I take a 95% confidence interval on this, and get a range of +-23.58.

So this means I have a 95% chance of having a win rate between $4.27 and $51.44?

The only problem I think that could happen here is its based on a normal curve. Is that a fair assumption?