NORM.S.DIST in WPS Spreadsheet: Standard Normal Probability and Density
Evaluate standard normal z-scores with an explicit cumulative flag, calculate central areas and avoid confusing the legacy one-argument form.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =NORM.S.DIST(1,TRUE) gives the standard normal lower-tail probability at z = 1, independently expected as 0.8413447461. =NORM.S.DIST(1,FALSE) gives the density height, about 0.2419707245. Include the second argument.
Syntax and the standard-normal model
=NORM.S.DIST(z,cumulative)
Both arguments are required. z is the evaluation point on a distribution with mean zero and standard deviation one. cumulative selects TRUE for cumulative probability or FALSE for density. There is no documented default for this required selector.
A raw measurement is not automatically a z-score. For a normal model with known mean μ and positive standard deviation σ, first calculate z = (x − μ)/σ. This function has no arguments for setting μ or σ; its standard model is fixed.
Example: compare cumulative and density outputs
Enter A2:A4 as −1, 0 and 1. In B2 enter =NORM.S.DIST(A2,TRUE) and fill down. In C2 enter =NORM.S.DIST(A2,FALSE) and fill down.
| Row | z | Independent B result: CDF | Independent C result: density |
|---|---|---|---|
| 2 | −1 | 0.158655253931457 | 0.241970724519143 |
| 3 | 0 | 0.5 | 0.398942280401433 |
| 4 | 1 | 0.841344746068543 | 0.241970724519143 |
The cumulative function increases with z. Density is symmetric and peaks at zero, so its values at −1 and 1 agree. Confusing those patterns is a common sign that the wrong Boolean was selected. Density is height, not the probability of exactly the supplied z-score.
Advanced example: standardize measurements and find a central area
Put x = 110 in F2, mean = 100 in F3 and standard deviation = 10 in F4. In G2 enter:
=NORM.S.DIST((F2-F3)/F4,TRUE)
The resulting z-score is 1, so the independent expectation is 0.841344746068543. Check F4 is positive before using this model. For density in the original measurement units, the corresponding expression is =NORM.S.DIST((F2-F3)/F4,FALSE)/F4, independently expected as 0.0241970724519143. Dividing by the standard deviation is essential when converting density back to original units.
For the central area between −1.96 and 1.96 use:
=NORM.S.DIST(1.96,TRUE)-NORM.S.DIST(-1.96,TRUE)
Independent expectation: 0.950004209703559. This is approximately 95%, not exactly 0.95 because 1.96 is a rounded quantile. The upper-tail expression =1-NORM.S.DIST(1.96,TRUE) is independently about 0.0249978951482204. These calculations do not by themselves justify a confidence interval or a hypothesis test; those require a suitable statistical design.
Errors, naming and limits
WPS documents #VALUE! for nonnumeric z. The reviewed source does not specify every omitted-argument, blank or non-Boolean case. Use literal TRUE/FALSE and complete numeric inputs rather than depending on undocumented conversions.
Do not drop the cumulative argument when converting from the legacy NORMSDIST(z) form: the dotted function explicitly has two arguments and offers both CDF and density. One source sentence misspells the name as NORMS.DIST, but its formal signature and walkthrough consistently use NORM.S.DIST. This guide follows the formal signature.
For the nonstandard mean-and-deviation interface, see the existing NORMDIST guide, while preserving its different exact function name. Mathematical correspondence is not a guarantee that every WPS spelling is interchangeable in every build.
Extreme tails can display as zero or one after rounding, and subtracting from one can lose relative precision in a very small tail. No native extreme-tail accuracy claim is made. Keep full intermediate values, choose the intended probability interval explicitly, and separate model assumptions from arithmetic verification.
Availability, version history and evidence
The official WPS NORM.S.DIST lesson was published 2019-06-18 and labels its applicable edition WPS Office for Windows Personal. The lesson was checked on October 19, 2026. This establishes a documented-by date, not the release in which the function first appeared. No numeric build, last supported version or retirement date is established. Mac, Linux, web, mobile and global-English edition parity are unverified.
Original expected results here are independent calculations or explicitly labelled test expectations, not native WPS execution. No WPS screenshot or installed-build test is claimed. Formula separators and displayed decimal precision can depend on the target setup; verify the exact function name in that installation before distributing a workbook.