Example: at most five support arrivals in one hour
Assume support arrivals follow a Poisson model with an average of three arrivals per hour. Ask for at most five in one hour.
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 Cumulative probability (CDF) for Calculation.
3. Enter the model
Enter 3 in Mean count (λ). This is the expected count in one hour.
4. Enter the question
Choose Single value for Value source. Enter 5 in Value (x). 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 expected count λ=3 in one hour. The question is the chance of at most five arrivals during that same hour.
Read the calculated value
CDF P(X ≤ x) is 0.916082, about 91.61%. It includes hourly counts from zero through five.
Understand what it means
Survival P(X ≥ x) is 0.184737 and includes five. The chance of more than five is the complement of the CDF: about 8.39%.
Use the model carefully
Check for busy periods, changing rates or clustered arrivals before using this model for staffing. The mean count must refer to the same one-hour interval.
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 counts up to x; Survival includes counts from x upward. Both include x. Survival P(X ≥ x) is 0.184737 and includes five. The chance of more than five is the complement of the CDF: about 8.39%.
| x | CDF P(X ≤ x) | Survival P(X ≥ x) |
|---|---|---|
| 5 | 0.916082 | 0.184737 |
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 | CDF |
| 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. Survival P(X ≥ x) is 0.184737 and includes five. The chance of more than five is the complement of the CDF: about 8.39%.
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.