The normal (Gaussian) distribution is the most important probability distribution in statistics. It is characterized by its bell-shaped curve, symmetric about the mean. Many natural phenomena follow a normal distribution, and it serves as the foundation for most statistical inference.

f(x) = 1/(σ√(2π)) × e^{-(x-μ)²/(2σ²)}

Where:
• μ = mean (center of distribution)
• σ = standard deviation (spread)
• The 68-95-99.7 rule: ~68% of data within 1σ, ~95% within 2σ, ~99.7% within 3σ

The z-score standardizes any normal distribution to the standard normal N(0,1): z = (x − μ) / σ. This calculator uses the rational approximation of the error function for accurate CDF values.