Example: a 90th-percentile waiting time
Assume exponentially distributed waits with a mean of twelve minutes. Find the time containing 90% of the modeled waits.
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 Inverse cumulative probability (quantile) 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 probability for Probability input source. Enter 0.9 in Cumulative probability. No worksheet columns are assigned.
5. Run analysis
Choose Run analysis, then open Results.
6. Interpret results
Check the question
Assume exponentially distributed waits with a mean of twelve minutes. Find the time containing 90% of the modeled waits.
Read the calculated value
The Quantile is about 27.63 minutes. This is a model percentile, not a confidence limit or a maximum wait.
Understand what it means
The result treats the entered mean of 12 minutes as given; uncertainty in an estimated mean is not included.
Use the model carefully
Under the stated model, 90% of waits are at or below about 27.63 minutes and 10% are longer. Compare that time with your waiting-time target and check that the model represents the operating period.
More details: read each result section
Complete result tables use six significant digits, as in Help.
Distribution quantiles
Probability target is the entered lower-tail probability. Quantile is the corresponding waiting time, in minutes. This is a model percentile, not a confidence limit or a maximum wait. Its accuracy depends on the entered mean and the waiting-time model.
| Probability target | Quantile |
|---|---|
| 0.9 | 27.631 |
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 | ICDF |
| 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. This is a model percentile, not a confidence limit or a maximum wait. Its accuracy depends on the entered mean and the waiting-time model.
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.