Example: a 95% cutoff for hourly support arrivals
Assume a Poisson model with three support arrivals per hour. Find a count that includes at least 95% of modeled hourly counts.
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, Poisson for Distribution, then Inverse cumulative probability (quantile) for Calculation.
3. Enter the model
Enter 3 in Mean count (λ). This is the expected count in one hour.
4. Enter the question
Enter 0.95 in Cumulative probability. Choose P(X ≤ x) for Tail. No worksheet columns are assigned.
5. Run analysis
Choose Run analysis, then open Results.
6. Interpret results
Check the question
Assume a Poisson model with three support arrivals per hour. Find a count that includes at least 95% of modeled hourly counts.
Read the calculated value
Critical x is 6. It is the smallest integer count for which P(X ≤ x) reaches at least 0.95.
Understand what it means
P(X≤5)≈91.61%, while P(X≤6)≈96.65%. Six is therefore the smallest count reaching the 95% target. Whole-number counts make cumulative probability rise in steps; six is not a maximum possible count.
Use the model carefully
Treat six as a model-based planning cutoff. Allow for the remaining upper tail and review whether the arrival rate stays comparable over time.
More details: read each result section
Complete result tables use six significant digits, as in Help.
Discrete critical value
Probability target is 0.95. Tail le means at most (X ≤ x). Critical x is the smallest integer reaching that target: P(X≤5)≈91.61%, but P(X≤6)≈96.65%.
| Probability target | Tail | Critical x |
|---|---|---|
| 0.95 | le | 6 |
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 | Poisson |
| Calculation | ICDF |
| Rate (λ) | 3 |
- Poisson(λ=3.0)
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. Whole-number counts make cumulative probability increase in steps. The probability at six can exceed 95%; six is not a maximum possible count.
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.