The Chauvenet test in the classical theory of errors

The so called W. Chauvenet rule [6] for rejection of outlying observations is transformed into a test in the case of normal random variables with unknown parameters.
It is shown that the distribution of the number of random variables $Y_1,\dots,Y_n$ (see section 2) which exceed some properly chosen critical value tends to a Poisson distribution as $n\to\infty$.