After the introduction of a new system of selection for study in the HEI, the issue of quality training of entrants has become very important. Motivated parents and students faced the problem of finding a school with highly qualified teachers or suitable tutors. Not all families can solve this problem. Thus, since 2008, a powerful non-random purposeful factor begins to form, which influences the formation of the stochastic value «scores of EIE certificates». Gradually, a subset of entrants is formed, which receives an additional opportunity to deservedly receive higher scores. For this subset of entrants, the law on normal distribution is certainly not revoked, but the average number of external evaluation points for this subset of entrants will be higher than that shown by entrants from another subset, consisting of those who, for one reason or another, did not receive access to the best teachers and tutors. The distribution of points of external examination certificates of these entrants will also be subject to the normal law, but with parameters that differ from those that characterize the distribution of the first subset of entrants.

The formation of these subsets is not carried out under the influence of random factors. There are purposeful non-random processes that destroy the homogeneity of the community of entrants, including:

• purposeful selection by parents for their children of schools where effective teachers work;
• providing their children with tutors who work with them in parallel with schooling.

The connection of these factors implies a high motivation of parents or relatives. And then they form a non-random community of students who have the best conditions for preparation for external independent evaluation. This community is heterogeneous in its cognitive abilities and motivation, so the test results will, of course, also is a stochastic value, which is subject to the normal law of distribution of points of external independent evaluation certificates with their parameters.

One of the significant factors in the deformation of the homogeneity of the community of entrants is the combination of indifference, passivity, demotivation of parents and students. This community is also heterogeneous in its cognitive abilities and the test results will also be a stochastic quantity with a normal distribution law. However, despite the indifference to learning and demotivation, some entrants from this community may get high scores, but on average they will not score high.