No, they don't loosely approximate. The experimental results are exceptionally close to the theoretical predictions. That's why it's a good theory.
As for getting it right, it's the best theory yet devised to describe subatomic particles. If you apply relativity theory to subatomic particles, you get bad results.
And that's the contradiction in physics. We need one theory (relativity) for large objects, and a different theory (quantum mechanics) for small objects.
Can you direct me to an article or book that describes these experiments? I’ve read several texts on quantum physics, and so far have found for the most part only theoretical discussion. It’s one thing to come up with a probabilistic treatment that can be reconciled mathematically with the known physical laws. Quite another thing to come up with a theory that can be tested favorably against actual statistics.
Maybe you are referring to the two slit experiments? I’m not sure if that convinces me. There are other explanations for that, as Bohm showed.