Standardnormalverteilungstabelle

The standard normal distribution, often referred to as the Gaussian distribution or the bell curve, is a specific type of normal distribution that is widely used in statistics and probability theory. It is characterized by its mean (μ) and standard deviation (σ). In the case of the standard normal distribution, the mean is 0 and the standard deviation is 1. This distribution is symmetric and unimodal, with the highest point at the mean.

The standard normal distribution is significant in statistics because many real-life phenomena can be approximated by it. This includes measurements such as height, weight, and IQ scores. The distribution is also fundamental in statistical inference, as it allows for the calculation of probabilities and the construction of confidence intervals.

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

f(x) = (1 / √(2π)) e^(-x²/2)

where x is a real number, π is the mathematical constant pi, and e is the base of the natural logarithm.

The cumulative distribution function (CDF) of the standard normal distribution, often denoted as Φ(x), gives the probability that a random variable X will take a value less than or equal to x. The CDF is related to the standard normal distribution table, which is a tabulated version of Φ(x) for various values of x.

The standard normal distribution is often used in hypothesis testing, where the null hypothesis is assumed to be true. The test statistic is then compared to the standard normal distribution to determine the p-value, which is the probability of observing the test statistic under the null hypothesis.

In summary, the standard normal distribution is a fundamental concept in statistics and probability theory. It is widely used in various fields, including science, engineering, and social sciences, due to its ability to approximate many real-life phenomena and its role in statistical inference.