normaalikäyrää

Normaalikäyrä, also known as the Gaussian curve or bell curve, is a fundamental concept in probability theory and statistics. It describes the probability distribution of a continuous random variable, where values are clustered around the mean and taper off symmetrically on either side. The shape of the curve is determined by two parameters: the mean (μ), which represents the center of the distribution, and the standard deviation (σ), which measures the spread or dispersion of the data.

The normal distribution is characterized by its distinctive bell shape. The highest point of the curve is at the mean, and the curve descends symmetrically on both sides, approaching the horizontal axis without ever touching it. A key property of the normal curve is that the area under the curve represents probability. Specifically, the area between two points on the horizontal axis corresponds to the probability that a random variable will fall within that range.

The empirical rule, often referred to as the 68-95-99.7 rule, is a useful guideline for understanding the normal distribution. It states that approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations. This rule highlights the predictable nature of data that follows a normal distribution.

The normal distribution is widely observed in nature and social sciences, appearing in phenomena such as measurement errors, heights of individuals, and IQ scores. Its prevalence and mathematical properties make it a cornerstone of statistical inference, hypothesis testing, and modeling in various fields.