I have a 1D normal distribution with mean $\mu$ and standard deviation $\sigma$. Given a new number $x$, I want to assign a confidence value to how likely $x$ is to have been drawn from the distribution $\mathcal{N}(\mu,\sigma)$
1 - the cdf gives me $P(X > x)$ but I'm not sure this is what I'm looking for.
Any help is much appreciated
EDIT
Just another thought, the value $x$ will fall on one side of the mean, or on the mean itself. Essentially I want to define a confidence measure that decreases to 0 as the point moves away from the mean, and is 1 at the mean. So what about $0.5 + f(x)$ where $f(x)$ is the pdf of the normal distribution between the bounds $\mu$ and $x$?
Thanks