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Imagine a widget factory. Every month they produce a truckload (population) of 3,300 widgets. If defective widgets are normally distributed, how many widgets must they examine to be 95% sure that **NO MORE THAN** 83 widgets (2.5% of the population) is defective? What is the answer? How does this generalize?

From another point of view, if the quality control widget guy decided that he only wanted to inspect 100 out of 3300 widgets, it would seem that he could be 95% certain that the total number of defects was bounded in some way. How does this work? What is the answer?

This sounds like a Z-test or T-test thing but since the population isn't set, I'm incredibly rusty, and Wikipedia is failing me on this one.