The central limit theorem (CLT) states that the sum of a large number of inependent and identically-distributed random variables will be approximately normally distributed (i.e., following a Gaussian distribution, or bell-shaped curve) if the random variables have a finite variance. Formally, a central limit theorem is any of a set of weak-convergence results in probability theory. They all express the fact that any sum of many independent identically distributed random variables will tend to be distributed according to a particular "attractor distribution".