I am trying to find a way to calculate the mean of my normal distribution if I know a certain percentile. Sounds simple, but I'm really stuck.
The purpose is to calculate a limit of detection (LD) based on Lloyd Currie's work on the issue and his proposal for a IUPAC definition. First, I calculate a critical value (LC) above which the chance of finding noise is less than e.g. 5%, so that I can control my false positives. Now, in order to control my false negatives, I define the LOD as the point above which a true signal will have a chance of less than e.g. 5% that an estimator falls below the LC.
So I have a value where a certain percentage has to be reached, and in order to achieve that, I need to set my mean (LD) accordingly. (The variance is fixed.)
My question is, can I do this mathematically somehow? In Excel and IDL, the only functions I've found were either for a standard normal distribution, or they needed the mean as an input and couldn't output it. And since the integral of the normal distribution is the error function, I can't simply solve the equation for µ.
Any ideas how to tackle this problem?