The Standard Normal distribution has a mean of 0 and a standard deviation of 1. The Standard Normal distribution is used in various hypothesis testing procedures such as tests on single means, the difference between two means, and tests on proportions. The standard normal curve is symmetrical, so the table can be used for values going in any direction, for example, a negative 0.45 or positive 0.45 has an area of 0.1736. Since probability tables cannot be printed for every normal distribution, as there is an infinite variety (families) of normal distributions, it is common practice to convert a normal to a standard normal and then use the standard normal table to find the required probabilities (area under the normal curve). A standard normal table is used to find the probability that a statistic is observed below, above, or between values on the standard normal distribution, and by extension, any normal distribution.
A standard normal table, also called the unit normal table or Z-table, is a table for the values of Φ calculated mathematically, and these are the values from the cumulative normal distribution function.
