This is really cool, any way you cut it.
With a quick bit of R code, we can simulate his PnL over 120 days multiple times, assuming he has no skill, and see what the probability of him being up 4k/day is. I'll use a t-distribution with 3 degrees of freedom, which allows big up and down swings (again, accentuating the effect of luck).
> pnl <- c()
> for (i in 1:1000) pnl[i] <- mean(2000 * rt(120, df=3))
> mean(pnl > 4000)