Normaaljaotusel

Normaaljaotusel, also known as the normal distribution or Gaussian distribution, is a continuous probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. It is a fundamental concept in statistics and probability theory, widely used in various fields such as finance, natural sciences, and engineering.

The normal distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ). The mean determines the location of the peak of the distribution, while the standard deviation controls the width of the distribution. The probability density function (PDF) of the normal distribution is given by the formula:

f(x; μ, σ) = (1 / (σ√(2π))) * e^(-(x - μ)^2 / (2σ^2))

where x is a real number, μ is the mean, σ is the standard deviation, π is the mathematical constant pi, and e is the base of the natural logarithm.

The normal distribution has several important properties. It is symmetric around the mean, and the total area under the curve is equal to 1. Approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations, a property known as the empirical rule or the 68-95-99.7 rule.

The normal distribution is often used to model real-world phenomena that are influenced by a large number of independent factors, such as measurement errors, natural phenomena, and financial returns. It is also the basis for many statistical tests and methods, including hypothesis testing, confidence intervals, and regression analysis.

In summary, the normal distribution is a widely used and important concept in statistics and probability theory, characterized by its symmetry, bell-shaped curve, and the empirical rule. It is used to model various real-world phenomena and serves as the foundation for many statistical methods.