This calculator finds a value's z-score and normal-distribution probability for students, researchers, and anyone comparing observations measured on different scales.
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Enter the observed value, population mean, and standard deviation, then choose the probability area you need, such as below, above, or between values.
The z-score is z = (value - mean) / standard deviation. Probabilities come from the standard normal distribution associated with that z-score.
A test score of 84 comes from a distribution with a mean of 72 and a standard deviation of 8. The z-score is (84 - 72) / 8 = 1.5, which is about the 93.32nd percentile.
It means the value is below the mean. A z-score of -1.2 places it 1.2 standard deviations below the mean.
No. Division by zero is undefined, and a zero standard deviation means every observation has the same value.
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