My, aren't we frisky tonight. :-)
No, 95 percent confidence in predicting the future is not what we have here. The problem boils down to this: Given a known prior history, what is the mathematical limit of accuracy for predictions regarding the immediate future i.e. what is the absolute bound on certainty for the prediction of the next state transition. In many (but not all) cases, the predictive accuracy rises above statistical chance with tractable datasets and computer systems. And given this, how good of a prediction can we actually make given some quantity of abstract computational resources to implement a predictor with i.e. bounding it to real implementation (hard problem, both math and engineering)? The effective limit on accuracy will vary as a function of a few parameters, not the least of which is the size of the machine acting as a predictor.
Do not think of this in terms of broad high-confidence predictions, though it is certainly possible, as that takes a hell of a lot of silicon to do. Think of it more in terms of a machine that can predict an apparently random boolean outcome 55 or 60% of the time for a complicated system. You don't have to predict correctly all the time, as even a slight bias toward correctly predicting systems that appear unpredictable will have a huge pay-off.
Interestingly, it has been known for decades that computers can predict individual human behavior better than other observing humans using simple induction, and often even when the human being observed is explicitly trying to be unpredictable.
I wrote a game based on this about 35 years ago. The computer tried to guess which choice a person would make (out of two.) It was very hard to beat the machine. Similarly, computers do wonders playing rock-scissors-paper (harder to program, but essentially the same.)