Suppose that x is the true time the operation takes. Then suppose that R is a random variable distributed uniformly on [0, 1000]. If I take a sample I will get values following the distribution x + R.

Then we calculate the sample mean of this distribution, X. Keep in mind that I can then set the number of samples to take to achieve my desired accuracy and confidence.

Then we look at the mean of the distribution x + R?

    E(x + R) = E(x) + E(R) = x + E(R) = x + 500

So therefore the true running time is recoverable by taking X - 500.