I’m not sure what you’re getting at here, so perhaps I’m misreading it. Quantum mechanics is an area where we do have a lot of verifiable observations, which is why we have accurate models that allow us to use calculations to design drugs and engineer semiconductor devices, lasers, and even rudimentary quantum information devices. As indicated in the OP, some of the outcomes are statistical, and that’s something we need to take into account in our measurements and engineering.
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