![]() Similarly, just over 95% of its probability density falls between -2 and +2 standard deviations. ![]() For example, 68.27% of values would fall between -1 and 1 standard deviations of a Z distribution. The fact that the distribution is standardized means that the quantiles are known, and that area between any two Z scores is also known. The Z distribution with key quantiles is shown on the graph below: The Z distribution is simply the standard normal distribution of the random variable Z meaning it is a normal distribution with mean 0 and variance and standard deviation equal to 1. Simply select "Z score from P" and enter the p-value threshold in the field to obtain the standard score defining the critical region. The z statistic calculator can also be used in inverse - to obtain a Z critical value corresponding to a given probability. The cumulative probabilities are calculated using the standard normal cumulative distribution function (CDF). ![]() The output also contains probabilities calculated for different areas under the standard normal curve which correspond to a one-tailed or two-tailed test of significance. If the variance is known instead, then the standard deviation is simply its square root. The z score calculator can be used to derive a z statistic from a raw score and known or estimated distribution mean and standard deviation.
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