NORMDIST in WPS Spreadsheet: Cumulative Probability or Density
Use explicit normal-distribution modes, standardize with the supplied mean and standard deviation and distinguish area from density height.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
NORMDIST evaluates a normal distribution with a supplied mean and standard deviation. Its final argument selects two fundamentally different outputs: a lower-tail probability or a probability density height. A density value is not the probability of observing exactly that number.
Syntax and modes
=NORMDIST(x, mean, standard_dev, cumulative)
The standard deviation must be positive. Use TRUE for the cumulative probability from negative infinity through x, and FALSE for the density at x. The original controls use explicit Booleans and moderate numeric arguments. The walkthrough prose misspells FALSE as “FLASE” in places; the formal syntax and density formula establish the intended Boolean FALSE, which is used here.
Standardize with z = (x − mean)/standard_dev. The density is exp(−z^2/2)/(standard_dev*sqrt(2*pi)); the factor 1/standard_dev is essential when changing scale.
Original example: mean 10, standard deviation 2
Enter 10 in B1 and 2 in B2.
- Use
=NORMDIST(12,B1,B2,TRUE). Since z=1, the independently expected lower-tail probability is approximately 0.841344746068543. - Use
=NORMDIST(12,B1,B2,FALSE)to calculate the density at 12, approximately 0.120985362259572. - Label the first as a probability and the second as density per unit of x. Do not percentage-format both as if they were the same quantity.
The probability at exactly 12 is zero in the continuous mathematical model. Probability over an interval comes from an area, found by subtracting cumulative values.
Independent controls
| Formula | Expected output, approximately |
|---|---|
=NORMDIST(10,10,2,TRUE) |
0.5 |
=NORMDIST(12,10,2,TRUE) |
0.841344746068543 |
=NORMDIST(8,10,2,TRUE) |
0.158655253931457 |
=NORMDIST(10,10,2,FALSE) |
0.199471140200716 |
=NORMDIST(12,10,2,FALSE) |
0.120985362259572 |
=NORMDIST(0,0,0.25,FALSE) |
1.59576912160573 |
The last density exceeds one without violating probability rules. Its total integrated area remains one; density height itself is not bounded by one.
Calculate an interval and check symmetry
Under mean 10 and standard deviation 2, the probability between 8 and 12 is the CDF at 12 minus the CDF at 8, approximately 0.682689492137086. The two endpoint CDFs also add to one because the endpoints are equally far below and above the mean.
These independent checks are useful for spotting a wrong standard deviation or an accidentally selected FALSE mode. They do not establish that a real dataset follows a normal distribution. Model assumptions and estimated parameters require separate justification; a function result alone does not justify a statistical decision.
Official demonstration and boundaries
The WPS example uses x=42, mean 40 and standard deviation 1.5, displaying cumulative 0.90878878 and density 0.10934005. The formula image and both outputs agree with the two-mode distinction. They are historical source observations, not tests of the original controls.
WPS documents #VALUE! for nonnumeric mean or standard deviation and #NUM! for nonpositive standard deviation. These controls avoid those errors and extreme tails. No modern dotted alias, cross-platform equivalence or application precision guarantee is inferred. For another normalized Gaussian-integral representation, see ERF, observing its different scaling and definition.
Availability and evidence scope
The official WPS lesson is dated 2019-05-24 and explicitly labels WPS Office for Windows Personal. Its numeric build is unspecified. This documents the function by that date; it does not establish first introduction, the last functioning build, other-platform parity or a retirement/deprecation history.
The complete lesson and its formula images and walkthrough were inspected on October 18, 2026. Original examples are documentation-derived independent calculations, not WPS or other spreadsheet-engine executions. Numeric reference values do not certify application precision or statistical model suitability.