A probability table is a type of mathematical table for the values of Φ. By definition, the values of Φ are the values of the cumulative distribution function (CDF or simply the "distribution function") of the normal distribution. Also known as the "standard normal table", "unit normal table", or the "Z table", the probability table is being used to determine the probability that a statistic is seen below, above, or between values on the standard normal distribution (and any normal distribution by extension).
A probability table can not be printed for each normal distribution. This is because there are an infinite variety of normal distributions. For this, a normal distribution can be converted to a standard normal distribution, where the latter table is being utilized to determine the probabilities.
By nature, normal distributions are symmetrical and bell-shaped distributions that are quite useful when it comes to describing realistic data. The letter “Z” is the one that represents the standard normal distribution. It is specifically defined as the normal distribution that has a mean of zero (0) and a standard deviation of one (1).
When it comes to reading a probability table or Z table, it should be noted that it is composed of the following elements:
- rows that are labeled with the integer part and the first decimal place of "Z"
- columns that are labeled with the second decimal place of "Z"
- values which correspond to the probabilities (calculations of the area under the normal curve from the starting point to Z) according to the table type