NORM.S.DIST
Return the probability that a standard normal value falls at or below z, or the height of the bell curve at z.
Syntax
NORM.S.DIST(z, cumulative)| Argument | Required | Description |
|---|---|---|
z | Required | The value, in standard deviations from the mean. |
cumulative | Required | TRUE for the probability of a value at or below z; FALSE for the density at z. |
Examples
Every example below was executed against VisiGrid engine 0.51.0 — not
transcribed from another vendor's documentation. Reproduce any of them with vgrid calc.
| Formula | Result | Notes |
|---|---|---|
=NORM.S.DIST(0,TRUE) | 0.50 | Half the distribution lies below the mean. |
=NORM.S.DIST(1.96,TRUE) | 0.98 | 97.5% — the familiar bound of a 95% two-sided interval, shown to two decimal places. |
=NORM.S.DIST(1,TRUE)-NORM.S.DIST(-1,TRUE) | 0.68 | About 68% of values lie within one standard deviation of the mean. |
=1-NORM.S.DIST((A2-B2)/C2,TRUE) | 0.02 | The share of an IQ-style scale (mean 100, sd 15) scoring above 130. |
=NORM.S.DIST(1,FALSE) | 0.24 | The height of the bell curve one standard deviation out. |
Standardise first
NORM.S.DIST works on the standard normal distribution: mean 0, standard
deviation 1. To use it on real data, convert the value to a z-score by
subtracting the mean and dividing by the standard deviation:
=NORM.S.DIST((130-100)/15,TRUE)Excel also has NORM.DIST, which takes the mean and standard deviation
directly, and NORM.S.INV, which goes from a probability back to z. Neither is
available here yet; the z-score conversion above covers the first.
Cumulative or density
With cumulative TRUE the result is a probability: the chance of a value at or
below z. That is almost always what you want. FALSE returns the height of the
curve at z, which is not a probability on its own — it is what you would plot to
draw the bell shape.
Precision
The cumulative value is computed with a standard approximation that is accurate to about seven decimal places. That is far below anything a two- or four-decimal display will show, but it is not Excel’s fifteen: at z = 1.96 the result differs from Excel’s in the eighth decimal place. For hypothesis tests and confidence intervals it makes no difference; for code that compares results to Excel’s at full precision, it will.
Excel compatibility
Matches Excel to about seven decimal places. Excel is accurate to about fifteen, so results differ past the seventh decimal.