CLT meaning in Governmental ?

In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution (informally a bell curve) even if the original variables themselves are not normally distributed. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions. This theorem has seen many changes during the formal development of probability theory. Previous versions of the theorem date back to 1811, but in its modern general form, this fundamental result in probability theory was precisely stated as late as 1920, thereby serving as a bridge between classical and modern probability theory.

If X 1 , X 2 , … , X n {\textstyle X_{1},X_{2},\dots ,X_{n}} are n {\textstyle n} random samples drawn from a population with overall mean μ {\textstyle \mu } and finite variance σ 2 {\textstyle \sigma ^{2}} , and if X ¯ n {\textstyle {\bar {X}}_{n}} is the sample mean, then the limiting form of the distribution, Z = lim n → ∞ n ( X ¯ reference