I agree 102% is not a possible value for the efficiency of the detector. But if the confidence interval traps the true value of the efficiency 95% of the time u

I agree 102% is not a possible value for the efficiency of the detector. But if the confidence interval traps the true value of the efficiency 95% of the time upon repeated sampling, what's the problem? That's all that's required for a confidence interval to be valid. Some CI constructions do in general give intervals that include impossible parameter values, but if they contain the true value 95% of the time, there's no issue. The coverage guarantee is all that matters. (One should not confuse a CI with a range of plausible values, in other words.)