Normal Tables

In statistics, a normal table, also known as a standard normal table or a z-table, is a table that provides probabilities associated with the standard normal distribution. The table lists values of the standard normal distribution's cumulative distribution function (CDF) for different values of the standardized variable Z.

A standard normal table typically provides probabilities for values of Z between -3.99 and 3.99 at intervals of 0.01. To use a standard normal table, one must find the corresponding row and column for a given Z-score and then read off the probability associated with that value of Z.

For example, if we want to find the probability of a Z-score less than or equal to 1.96, we would look for the row corresponding to 1.9 and the column corresponding to 0.06 in the standard normal table. The value at the intersection of the row and column is 0.9750, which indicates that the probability of a Z-score less than or equal to 1.96 is 0.9750, or 97.5%.

The standard normal table is helpful in statistical inference and hypothesis testing, where it is often used to calculate critical values and p-values associated with the standard normal distribution. It is also used to calculate confidence intervals and in various statistical models, such as linear and logistic regression.