That's the reason it is expected to have 5 sigma, so that anomalies are extremely rare. The more experiments one makes, the closer one gets to the mean value and this happens exponentially fast. By that, I mean that using some probability theory and some algebra you can get a confidence bound on the accuracy you demand based on the number of experiments that you run.
I would like to point you towards Hoeffding's inequality. The probability of deviating more than epsilon from the mean after n experiments is exponential in n.
