Sorry if the question is phrased awkwardly, I'm not sure what to properly call the question.
Here's my question:
$X$ is a normal distribution ~$N(0,\sigma^2)$
$P( X < A ) = P( A < X < B )$
A and B are 2 (negative) numbers that are given.
Basically, it's that for a given range $A$ to $B$, the normal distribution has the cumulative probability of the left-tail below $A$ equal to the cumulative probability of the range $A$ to $B$. How do I calculate the variance, $\sigma^2$?
For what it's worth, I've been able to get:
$Z$ ~ $N(0,1)$
$P( Z < -A/\sigma ) = x$
$P( Z < -B/\sigma ) = 2x$
I don't know if I'm even on the right track though.