Question

Hello Rabbi Michi,
If I understand correctly, the law of large numbers says (not the most precise definition) that if you observe an infinite sequence of random observations that are independent of one another, all describing the same phenomenon, then the average of the sequence will get closer and closer to a fixed value.
Let’s take an example: in a sufficiently large sample of people with a certain characteristic, the average will resemble that of the general population from which the sample was taken.
Nadav Shnerb once wrote about this in connection with education (in Makor Rishon): “The educational activity that these people imagine can be carried out only by people who are themselves people of high caliber, and it seems that everyone understands that in a system of mass education, with hundreds of thousands of teachers, there is simply no possibility of achieving this goal. The law of large numbers guarantees that the teachers will be more or less a representative sample of society (perhaps excluding truly very low strata, but not much more than that), and therefore the typical teacher will not be a more moral person or serve as a better personal example than the average parent.”
The questions are as follows:
A) Obviously the value of the sample is percentage-based and not absolute, so what is the threshold for sample size at which one could make Shnerb’s claim?
B) Is it possible to influence the law by means of an education system, incentives, and the like? Take engineers for example: if through education and economic and social incentives, etc., we cause all 10% (let’s say that’s the threshold from question 1) of the population who have above-reasonable engineering ability to become engineers, does that mean that the average ability of an engineer will equal the average engineering ability of the population? That seems to contradict common sense, doesn’t it?
If the answer is yes, then Shnerb’s claim falls apart, because if we manage to cause most teachers to come from the more value-oriented percentiles, then the average level of values will be higher than the average level of values in the population. And even if we say that isn’t realistic, at the very least we could reduce the size of the sample and try to take only the principals and homeroom teachers from the more value-oriented percentiles of the population.
 
Thanks,
N
Link to Shnerb’s remarks