Find normal-distribution probabilities for a value — cumulative, upper tail, and density. Enter the value, mean, and standard deviation.
P(X ≤ x)
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Cumulative probability.Usage Tip
The famous 68-95-99.7 rule: about 68, 95, and 99.7 percent of data lie within 1, 2, and 3 standard deviations of the mean.
THE MATH
z = (x − mean) ÷ sd
Cumulative probability from the standard normal curve
Cumulative probability from the standard normal curve
The normal (bell) curve describes many natural measurements.
The cumulative probability is the area under the curve up to a value; the density is the curve height there.
The cumulative probability is the area under the curve up to a value; the density is the curve height there.
The standard deviation must be positive.
P(X less than or equal to x) is the area to the left; P(X greater than x) is to the right.
Probabilities are approximate (error-function based).
P(X less than or equal to x) is the area to the left; P(X greater than x) is to the right.
Probabilities are approximate (error-function based).