This calculator finds probabilities, percentiles, and ranges for normally distributed measurements used in statistics, testing, and quality control.
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Enter the distribution mean and standard deviation, then supply a value or lower and upper bounds. Select whether you want the probability below, above, or between those limits.
Convert each value to the standard normal scale with z = (value - mean) / standard deviation. The cumulative probability is P(X ≤ x) = Φ(z), and a probability between two values is Φ(z upper) - Φ(z lower).
Suppose package weights are normally distributed with a mean of 500 g and a standard deviation of 10 g. The probability of a package weighing between 490 g and 510 g is Φ(1) - Φ(-1), or about 68.27%.
Find the cumulative probability below the value, then subtract it from 1. In symbols, P(X > x) = 1 - Φ(z).
Normal-distribution probabilities may then be misleading, especially in the tails. Check a histogram, normal probability plot, or a model suited to the data's actual shape.
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