Suppose that I have a normally distributed variable with unknown mean and known SD: $X \sim N(\mu, 1)$. I also know that $P(-2 < X < 2) = 0.3.$ Is it possible to calculate $\mu$ from this information alone?
As best I can tell, it isn't possible, because $\mu$ is not identified. But I am unsure of my thinking on this point. Normal Distribution - finding mean takes up a related question, but in that question, one has more information about X.