I am writing a report for my boss quoting the success rates for tests of various components. If something works 19 times out of twenty, then it's 95%. But what is the uncertainty on this? 95% +/- ? And if a component passes every test (100%), what is the lower limit on the actual rate? How many tests must we do to be confident it is above 95%? The assumption is that the probability of success is a fixed value, and the uncertainty on our estimate of this is just limited by the number of tests done.