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math.stats-normal-distribution Calculator
Calculates the probability that a normally distributed variable falls within a given range, using the standard normal table (erf). The Central Limit Theorem says sample means are normally distributed regardless of the underlying distribution — this connects that theorem to a calculable number.
Inputs
X
Reference formula or conversion factor shown for context.
Mu
Arithmetic average. Sensitive to outliers — if your data has extreme values, the median may be more representative.
Sigma
Reference formula or conversion factor shown for context.
Results
PDF f(x)
Reference formula or conversion factor shown for context.
z-score
Number of standard deviations a value is from the mean. |z| below 2: within normal range. |z| above 2: in the outer 5% of the distribution. |z| above 3: in the outer 0.3%.
peak at \u03bc
The value at the specified point or condition.
CDF P(X≤x)
Reference formula or conversion factor shown for context.