ZTabellen

ZTabellen, often referred to as Z-Tabellen or standard normal distribution tables, are reference resources used in statistics to find probabilities associated with the standard normal distribution. The standard normal distribution, denoted Z ~ N(0,1), has a mean of 0 and a standard deviation of 1. The table tabulates the cumulative distribution function Phi(z) = P(Z ≤ z) for values of z. In classic formats the table is organized with z-values in the rows and columns representing the second decimal place, allowing interpolation for values in steps of 0.01. Some tables present only positive z-values and rely on symmetry, since Phi(-z) = 1 − Phi(z). Other variants display upper-tail probabilities P(Z > z) = 1 − Phi(z).

To use the table, one typically converts a measured value into a z-score: z = (X − μ) / σ. The table then provides the probability that Z is less than or equal to z, which serves as a p-value for one-sided tests or can be adapted for two-sided tests. Z-Tabellen are also used to determine critical z-values for a given significance level and to construct confidence intervals when the standard deviation is known.

Limitations include the fact that tables are approximations and require interpolation for values not exactly listed. With modern tools, software and calculators compute Phi(z) directly, reducing the need for physical tables. Nonetheless, ZTabellen remain a foundational teaching aid for illustrating the properties of the standard normal distribution and for quick, hand calculations in introductory statistics.