CRITBINOM in WPS Spreadsheet: The First Binomial CDF Crossing
Find the smallest success count whose cumulative binomial probability reaches alpha, verify adjacent counts and distinguish a discrete quantile from interpolation.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
CRITBINOM returns the smallest integer success count whose cumulative binomial probability is at least alpha. It is an inverse count operation: its output is a count, while alpha is a probability threshold. It does not interpolate between counts to force the cumulative probability to equal alpha exactly.
Syntax and model assumptions
=CRITBINOM(trials, probability_s, alpha)
Trials is the fixed number of independent Bernoulli trials. Probability_s is the constant probability of success on each trial. Alpha is the desired lower-tail cumulative threshold. Original controls use small positive integer trials and probabilities strictly inside zero and one.
The same word “success” can label any event being counted, including a defect in a hypothetical quality model. The function does not decide what event should be labeled success or guarantee product quality. Its output must be interpreted within a separately specified sampling plan.
Original four-trial example
For four trials with success probability 0.5, the point probabilities for counts 0 through 4 are 1, 4, 6, 4, 1 divided by 16. The cumulative probabilities are:
| Count k | P(X≤k) |
|---|---|
| 0 | 1/16 |
| 1 | 5/16 |
| 2 | 11/16 |
| 3 | 15/16 |
| 4 | 1 |
- Enter 4 in A2, 0.5 in A3 and 0.5 in A4.
- Use
=CRITBINOM(A2,A3,A4)in B2. - At count 1 the CDF is 0.3125, below 0.5.
- At count 2 the CDF is 0.6875, meeting the threshold.
- The independently expected result is 2.
Checking both the returned count and the preceding count establishes the “smallest” part of the contract.
Independent controls
| Formula | Expected count | Crossing explanation |
|---|---|---|
=CRITBINOM(4,0.5,0.5) |
2 | 5/16 < 0.5 ≤ 11/16 |
=CRITBINOM(4,0.5,0.3125) |
1 | CDF equals the threshold at 1 |
=CRITBINOM(4,0.5,0.3333333333333333) |
2 | Threshold just above 5/16 |
=CRITBINOM(4,0.5,0.9) |
3 | 11/16 < 0.9 ≤ 15/16 |
=CRITBINOM(3,0.25,0.5) |
1 | 27/64 < 0.5 ≤ 54/64 |
=CRITBINOM(3,0.75,0.5) |
2 | 10/64 < 0.5 ≤ 37/64 |
The decimal one-third input lies safely away from a CDF jump, so its rounding does not change the expected crossing. The exact 0.3125 case directly checks “greater than or equal to.”
Why discrete thresholds jump
Every alpha above 5/16 and at or below 11/16 has the same result 2 in the four-trial example. A tiny alpha change across 5/16 changes the count abruptly; interpolation to a fractional count would answer a different question.
The result 2 does not mean a 50% probability of exactly two successes. That point probability is 6/16=0.375. Nor does it imply that exactly two successes will occur in an actual run of four trials. It identifies a cumulative threshold in a model.
Vendor corroboration and limits
The official example trials=7, probability=0.6 and alpha=0.85 returns 6. Independently, the CDF through 5 is 0.8413696 and through 6 is 0.9720064, so 6 is the first crossing. The narrative’s output-cell reference differs from the screenshot; the original layout above avoids that ambiguity.
The lesson describes truncating trial counts and error conditions for malformed inputs. Original controls avoid endpoints, fractional trials and coercion. No modern BINOM.INV alias is assumed. PROB can sum a supplied discrete distribution, while PERCENTILE uses an empirical interpolation contract rather than this binomial count rule.
Availability and evidence scope
The official WPS lesson is dated 2019-08-22 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.