A z-score of 15 gives a p-value (using R) of:
> pnorm(15, lower.tail=FALSE)  3.670966e-51
Assuming you haven't done anything wrong, like feeding it the wrong attribute value or constructing a silly adjacency matrix, I'd say that was significant. Note that Moran's I will usually be significant if there's a large-scale trend in the data, so make sure you plot the map and eyeball anything like that first, then detrend it and look for residual spatial correlation with your Moran I then.
I'd also only ever say
p < 0.01 in this sort of case.
Also, I assume that diagram of a Normal distribution is just illustrative. Your data is FIFTEEN standard deviations from the mean. On my screen, that would put it somewhere in the next door office :)