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Computing per cent correctness from a bell curve

I've been trying to remember my High School teachings and are falling short.

I'm working on a project where I need to give a % of correctness for an integer (How close a given number is to the actual number within a 300% difference). For example if real number is 50, any number from -100 to 150 will return > 0% correctness.

The problem is that we need a curve (log, or bell curve, or something similar) to return a non-linear % correctness (i.e. 100 is 50% correct in linear terms, but we would want maybe 66%? ... and 125 is 33%?) and I dont have a formula to get this response.

Something like this (sorry, used mspaint quickly to try to explain) Example

Am I explaining this properly? Make sense? Any help? ;)

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Tizz
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  • I think what you're looking for is called "standard deviation". http://www.mathsisfun.com/data/standard-deviation.html –  Oct 13 '11 at 19:40
  • Yep, I ran into standard deviation too, just its a bit complicated for me to process right now. If you understand it, can you throw me a formula? :) – Tizz Oct 13 '11 at 20:17
  • I don't think what you're asking for is a standard mathematical concept. Maybe if you can explain why you need this, we can recognize the concept you are thinking of. –  Oct 13 '11 at 21:31

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