normaldistributie

Normaldistributie, also known as the Gaussian distribution or bell curve, is a fundamental probability distribution in statistics. It is characterized by its symmetric, bell-shaped curve, which is centered around its mean. The shape of the normal distribution is determined by two parameters: the mean (μ) and the standard deviation (σ). The mean represents the center of the distribution, while the standard deviation quantifies the spread or variability of the data.

The probability density function (PDF) of the normal distribution is given by the formula:

f(x | μ, σ) = (1 / (σ sqrt(2π))) exp(-((x - μ)^2 / (2σ^2)))

This formula describes the likelihood of observing a particular value 'x' within the distribution. A key property of the normal distribution is that approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations. This is often referred to as the empirical rule or the 68-95-99.7 rule.

The normal distribution is widely observed in nature and many human-made phenomena. Examples include heights of people, measurement errors, and test scores. Its prevalence and mathematical properties make it a cornerstone for statistical inference, hypothesis testing, and modeling in various scientific and engineering disciplines. Many statistical methods rely on the assumption that the data being analyzed follows a normal distribution.