Example: at most two nonconforming labels
Inspect 25 independent labels, each with an assumed 4% chance of nonconformance. Ask for at most two nonconforming labels.
Download the scenario reference (CSV)This is the same example used in Help. The CSV lists reference scenarios. Enter the selected scenario manually on Inputs; importing it does not configure this calculator. Use Open example in a practice copy in Help to prefill the inputs.
1. Create the workspace
In the sidebar, open Basic Statistics and choose Distributions. Create an analysis, name it, select New blank worksheet, then choose Create analysis.
2. Choose the calculation
On Inputs, choose Discrete for Distribution type, Binomial for Distribution, then Cumulative probability (CDF) for Calculation.
3. Enter the model
Enter 25 in Number of trials (n) and 0.04 in Success probability (p). Here a “success” means finding a nonconforming label.
4. Enter the question
Choose Single value for Value source. Enter 2 in Value (x). No worksheet columns are assigned.
5. Run analysis
Choose Run analysis, then open Results.
6. Interpret results
Check the question
Inspect 25 independent labels, each with an assumed 4% chance of nonconformance. Ask for at most two nonconforming labels.
Read the calculated value
CDF P(X ≤ x) is 0.923517, about 92.35%. It adds the chances of finding zero, one or two nonconforming labels.
Understand what it means
Survival P(X ≥ x) is 0.264190. It includes two as well, so the two displayed tails overlap. The chance of more than two is 1 − 0.923517 = 0.076483, about 7.65%.
Use the model carefully
Use the probability that matches the decision rule. Check the assumed 4% rate and independence before applying it to another batch.
More details: read each result section
Complete result tables use six significant digits, as in Help.
Distribution values
x is the cutoff count. CDF includes X ≤ x; Survival includes X ≥ x. Both contain the exactly-x case. Use the worked comparison above to distinguish the inclusive upper tail from the complement 1 − CDF.
| x | CDF P(X ≤ x) | Survival P(X ≥ x) |
|---|---|---|
| 2 | 0.923517 | 0.26419 |
Distribution summary
Type distinguishes continuous values from whole-number counts. Distribution names the model. Calculation records PMF (exact-count probability), PDF (density), CDF (cumulative probability) or ICDF (quantile). The remaining rows record the active parameters; they are assumptions entered on Inputs.
| Setting | Value |
|---|---|
| Type | Discrete |
| Distribution | Binomial |
| Calculation | CDF |
| Number of trials (n) | 25 |
| Success probability (p) | 0.04 |
- Binomial(n=25, p=0.04)
7. Create a report
Keep Distribution values (or the quantile table) and Distribution summary. State the model assumptions, time unit or count interval, and the question being answered. Survival P(X ≥ x) is 0.264190. It includes two as well, so the two displayed tails overlap. The chance of more than two is 1 − 0.923517 = 0.076483, about 7.65%.
Choose Add to report from the completed run. Open Choose individual items and advanced options to select tables and charts, then choose Add to draft. Hidden items stay in the saved analysis.
Name the report and add the purpose of the study and your interpretation. Choose Save, review Preview, then use Export → Download HTML. The example below contains the full selected content, including results beyond one screen.