LOGNORMDIST in WPS Spreadsheet: Log-Scale Cumulative Probability
Calculate a lognormal lower-tail probability with parameters for ln(x), distinguish the median from the raw mean and check the normal transformation.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
LOGNORMDIST returns a lognormal cumulative probability. The defining WPS relationship is that ln(x), rather than x itself, follows a normal distribution with the supplied mean and standard deviation. Mixing raw-scale and log-scale parameters changes the model.
Syntax and parameter scale
=LOGNORMDIST(x, mean, standard_dev)
All three arguments are required. Original examples use x greater than zero and a positive standard deviation. Mean and standard_dev describe ln(x). The formula image gives the standard-normal cumulative probability at (ln(x)−mean)/standard_dev.
This legacy signature returns a cumulative probability only; it has no density flag. No modern dotted alias or extra argument is assumed. The screenshot loosely labels its third input as a variance, but the formal text and equation identify a standard deviation. Do not square the supplied standard deviation merely to match that loose label.
Original worked example
Suppose the model for ln(x) has mean 1 and standard deviation 0.5.
- Enter
=EXP(1.5)in A2, 1 in B2 and 0.5 in C2. - Use
=LOGNORMDIST(A2,B2,C2)in D2. - Independently, ln(x)=1.5, so z=(1.5−1)/0.5=1.
- The expected lower-tail probability is approximately 0.841344746068543.
The x input is about 4.48168907034 on the original scale. The result is the model probability of a value at or below that threshold, not the logarithm of a probability.
Independent controls
| Formula | Standardized log value | Expected cumulative probability |
|---|---|---|
=LOGNORMDIST(EXP(1),1,0.5) |
0 | 0.5 |
=LOGNORMDIST(EXP(1.5),1,0.5) |
1 | 0.841344746068543 |
=LOGNORMDIST(EXP(0.5),1,0.5) |
−1 | 0.158655253931457 |
=LOGNORMDIST(EXP(0),0,1) |
0 | 0.5 |
=LOGNORMDIST(EXP(1),0,1) |
1 | 0.841344746068543 |
=LOGNORMDIST(EXP(2),1,1) |
1 | 0.841344746068543 |
The same standardized log value gives the same cumulative probability even when the original-scale threshold changes. These are independently calculated controls, not captured application results.
Interval probability and scale interpretation
For the first model, the probability between exp(0.5) and exp(1.5) is the difference of the endpoint CDFs, approximately 0.682689492137086. On the original scale that interval is about 1.64872 to 4.48169. It is multiplicatively symmetric around exp(1), not additively symmetric around the raw arithmetic mean.
The median is exp(1), approximately 2.71828, because its CDF is one half. The mathematical raw mean of this lognormal model is exp(1+0.5²/2), approximately 3.08022. Therefore the argument named mean is neither of those raw-scale summaries. Using an observed arithmetic mean directly as the log-mean parameter would generally be incorrect.
Source example, errors and limitations
The vendor example uses x=20, mean=5 and standard deviation=0.125, displaying 3.6898E−58. Its formula and inputs support the log-scale transformation. That extreme displayed probability does not certify general extreme-tail accuracy; the original examples use moderate standardized values.
WPS documents #VALUE! for nonnumeric arguments and #NUM! when x or standard deviation is nonpositive. Original controls do not execute those errors or test coercion. A fitted lognormal model requires independent justification; positivity of data alone does not prove lognormality.
See NORMDIST for the underlying normal-model distinction between density and cumulative probability, and EXP for exponentiation on the original scale.
Availability and evidence scope
The official WPS lesson is dated 2019-06-19 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 official lesson was rechecked on October 19, 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.