\(x\) is the value we are standardizing, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.A z-table, also called standard normal table, is a table used to find the percentage of values below a given z-score in a standard normal distribution.Ī z-score, also known as standard score, indicates how many standard deviations away a data point is above (or below) the mean.Ī positive z-score implies that the data point is above the mean, while a negative z-score indicates that the data point falls below the mean. The formula for calculating a Z-value is: Z-values express how many standard deviations from the mean a value is. The standard normal distribution is also called the 'Z-distribution' and the values are called 'Z-values' (or Z-scores). Typically, probabilities are found by looking up tables of pre-calculated values, or by using software and programming. The functions for calculating probabilities are complex and difficult to calculate by hand.
Standardizing makes it easier to calculate probabilities. Here is a graph of the standard normal distribution with probability values (p-values) between the standard deviations: The standard normal distribution is used for: Standardizing normally distributed data makes it easier to compare different sets of data. Normally distributed data can be transformed into a standard normal distribution. The standard normal distribution is a normal distribution where the mean is 0 and the standard deviation is 1. Stat Reference Stat Z-Table Stat T-Table Stat Hypothesis Testing Proportion (Left Tailed) Stat Hypothesis Testing Proportion (Two Tailed) Stat Hypothesis Testing Mean (Left Tailed) Stat Hypothesis Testing Mean (Two Tailed)
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