I have burned 200 disks and I want to make sure that they are all in perfect working order. What is the smallest size sample I could test in order to be relatively confident that 98% of all the disks are fine/burned correctly?
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There isn't enough information to answer the question. Even if you specify a level of confidence you'd like to reach, there's no way of calculating your confidence after the test without knowing your assessment of the reliability of the burner before the test. For instance, if you think a priori that the burner is 1% likely to be defective and make a mistake on every tenth disk and 99% likely to be perfect and never make mistakes, you'll have a different confidence after the test than if you think a priori that the burner is 50% likely to be defective and 50% likely to be perfect. This difference will exist no matter what the test results are and no matter how many of the disks you check (unless you check 98% of them and find them all to be OK). So this isn't a well-defined problem without a specification of your prior assessment.