It is common practice to convert any normally distributed data to the standard normal distribution as the standard normal distribution table contains a value for every standardized z-score. More specifically, the table contains values for the cumulative distribution function of the standard normal distribution at a given value, x. between negative infinity and Z).A standard normal distribution table, also known as the unit normal table or Z table, is used to find the probability that a statistic is observed below, above, or between values in the standard normal distribution, the so-called p-value. This table gives a probability that a statistic is less than Z (i.e. Note that for z = 1, 2, 3, one obtains (after multiplying by 2 to account for the interval) the results f ( z) = 0.6827, 0.9545, 0.9974, If X is a random variable from a normal distribution with mean μ and standard deviation σ, its Z-score may be calculated from X by subtracting μ and dividing by the standard deviation: The standard normal distribution, represented by Z, is the normal distribution having a mean of 0 and a standard deviation of 1. Normal distributions are symmetrical, bell-shaped distributions that are useful in describing real-world data. Since probability tables cannot be printed for every normal distribution, as there are an infinite variety of normal distributions, it is common practice to convert a normal to a standard normal (known as a z-score) and then use the standard normal table to find probabilities. It 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. In statistics, a standard normal table, also called the unit normal table or Z table, is a mathematical table for the values of Φ, the cumulative distribution function of the normal distribution. Table of probabilities related to the normal distribution
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