However, the 7 here is basically (x - mu)/sigma, so it is normalised (in that sense), anyway.
A good example is efficiency measurements. I can't count how often I have seen students say something like: Our detector is 99%+-3% efficient. Obviously a detector can't be 102% efficient.
I have a master's degree in statistics and this is the first I'm hearing about it.
> Our detector is 99%+-3% efficient. Obviously a detector can't be 102% efficient.
In the absence of any other context I'd guess that they're using an approximation to a confidence interval that might be perfectly fine if the estimated value was nearer the center of the allowable range.
Hearing 99+-3% is a very strong indication that the person used an incorrect way to determine the uncertainty, most likely by taking the square-root of counts. But you are right, if the efficiency would be around 50%, that approximation is not so bad.
(One should not confuse a CI with a range of plausible values, in other words.)
