# calculate mean of normal distribution given SD and probability corresponding to a single range

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.