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The standard normal distribution table , or z table , provides probabilities for the standard normal distribution . The standard normal distribution is just a special case of the widely used normal distribution . The normal distribution is widely used for two reasons. The first reason is that it has a lot of real-world applications. Many everyday things, such as test scores, height, weight, rainfall and so on, are normally distributed. Secondly, the normal distribution is used frequently in the ... t Distribution Critical Values −6 −4 −2 0 2 4 6 ... χ2 Distribution Critical Values χ(ν) 2 Normal distribution to standard normal distribution : When working with the normal distribution , it can be useful to convert to the standard normal distribution , which has a mean of 0 and a standard deviation of 1. The z- table is built based on the standard normal distribution . Find the percentage of values below a given z-score in a standard normal distribution .