Confidence Intervals for Pass Rates

The job ticket assistant passes 45 of 50 test cases, which is 90 percent. One common method says the true pass rate is plausibly anywhere from 81.7 to 98.3 percent. A second method, applied to the same 45 of 50, says from 78.6 to 95.7 percent.

The two ranges differ by about 3 points at each end, and the difference is not a rounding detail. Near 0 or 100 percent, the first method produces ranges that are impossible or falsely certain. Those are exactly the rates a team sees on its most important checks.