On the methodology of verification of adequacy of the central limit theorem
The paper presents the methodology of verification of adequacy of the central limit theorem based on the connection of the latter with Bernoulli's theorem. The proposed methodology has an advantage over direct verification of adequacy of the central limit theorem because verification of adequacy of Bernoulli's theorem requires considerably less efforts than verification of any limit theorem in probability theory. However, the central limit theorem is much more effective than Bernoulli's theorem.