The normal distribution is a continuous probability function defined by its mean and standard deviation, exhibiting symmetry around the arithmetic mean where approximately 68% of data points lie within one standard deviation from the center. As a fundamental subfield of mathematical statistics, it relies on formal parameters μ (mean) and σ² (variance) to describe bell-shaped curves underpinned by the Central Limit Theorem, which asserts that sums of independent random variables converge toward this specific limiting distribution regardless of individual underlying distributions.
Explains the normal distribution: the bell curve's mean and standard deviation parameters, symmetry, how probabilities correspond to areas, and why it appears throughout statistics.