standard normal table z score how to use

For example, a Z-score of 1 means that the value is 1 standard deviation from the mean. The resulting distribution of Z-scores is referred to as a Z distribution (or standard normal distribution), where the Z-score represents the number of standard deviations (not the value of the standard deviation) that a given value is from the mean. Where μ is the mean, σ is the standard deviation, and x is the value being converted.

Z-scores and Z distributionsĪ normally distributed random variable can be standardized by converting its values to Z-scores using the following formula, However, since all normal distributions can be converted to a standard normal distribution, and since the associated probabilities have already been computed and compiled into Z tables for a standard normal distribution, it is possible to reference Z tables rather than having to integrate the pdf to determine the probability of outcomes within a given interval occurring. This is useful because, typically, it is necessary to integrate the probability density function (pdf) of a random variable to determine the probabilities of outcomes within an interval for the case of a normal distribution, this is particularly difficult. It tells us the probability that values in a normal distribution lie below, above, or between values on the standard normal distribution. Home / probability and statistics / hypothesis test / z table Z tableĪ Z table, also referred to as a standard normal table, is a table of the values of the cumulative distribution function of a normal distribution.

Standard normal table z score how to use