I have a single observation with value $x = 0.5$ that comes out from a complicated computational process. I would like to know what is the probability to observe such value by chance.
To attempt to answer the question, I have ran the computational process with random input values for few thousand times. I get a distribution that is about normal, has mean very close to zero, and a standard deviation around 0.09.
Intuitively, it looks like the chance of observing 0.5 by chance is very little. However, how do I turn this into an actual statistical test?