Example: waiting more than twenty minutes
Assume the wait to the next arrival follows an exponential model with a mean of twelve minutes. Ask for a wait longer than twenty minutes.
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 Continuous for Distribution type, Exponential for Distribution, then Cumulative probability (CDF) for Calculation.
3. Enter the model
Choose Mean θ for Exponential parameter. Enter 12 in Mean (θ), in minutes.
4. Enter the question
Choose Single value for Value source. Enter 20 in Value (x), in minutes. No worksheet columns are assigned.
5. Run analysis
Choose Run analysis, then open Results.
6. Interpret results
Check the question
Assume the wait to the next arrival follows an exponential model with a mean of twelve minutes. Ask for a wait longer than twenty minutes.
Read the calculated value
The displayed CDF is 0.811124: about 81.11% of modeled waits are at or below twenty minutes.
Understand what it means
For more than twenty minutes, subtract the CDF from one: 0.188876, about 18.89%. Twelve is the mean waiting time, not a rate of twelve arrivals per minute.
Use the model carefully
Under the stated exponential model, about 18.89% of waits exceed 20 minutes. Check whether a constant arrival rate is reasonable before applying this answer, and keep the mean and cutoff in minutes.
More details: read each result section
Complete result tables use six significant digits, as in Help.
Distribution values
x is the entered waiting time in minutes. CDF is P(X ≤ x); its complement answers the requested longer-than question. For more than twenty minutes, subtract the CDF from one: 0.188876, about 18.89%. Twelve is the mean waiting time, not a rate of twelve arrivals per minute.
| x | CDF |
|---|---|
| 20 | 0.811124 |
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 | Continuous |
| Distribution | Exponential |
| Calculation | CDF |
| Mean (θ) | 12 |
- Exponential(mean θ=12.0) via expon(scale=θ)
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. For more than twenty minutes, subtract the CDF from one: 0.188876, about 18.89%. Twelve is the mean waiting time, not a rate of twelve arrivals per minute.
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.