The Central Limit Theorem establishes that, in most situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a "bell curve" or Gaussian) even if the original variables themselves are not normally distributed.
Intro to Statistics
These thoughts were extracted from Udacity online course and cover topics such as: Visualizing relationships in data, Probability, Estimation, Outliers and Normal Distribution, Inference and Regression.