Understanding Uniform Distribution Probability
A uniform distribution describes a random value spread evenly across a fixed interval. Every equal length inside the interval has the same chance. This makes the model simple, fair, and useful for many statistics lessons.
What This Calculator Does
This calculator finds probabilities for continuous uniform distributions. You enter a lower bound and an upper bound. Then you choose a probability question. The tool can evaluate left tail, right tail, between values, outside values, density, point probability, and quantiles. It also reports mean, median, variance, and standard deviation.
Why the Bounds Matter
The lower and upper bounds define the full possible range. Values below the lower bound have zero cumulative probability. Values above the upper bound have full cumulative probability. Values inside the interval rise in a straight line. Because the density is constant, probability depends only on interval length.
Practical Uses
Uniform models appear when outcomes are equally likely inside limits. They are common in random number generation, waiting time approximations, simulation inputs, quality checks, and classroom examples. The model also helps compare simple continuous probability with more complex distributions.
Interpreting the Result
For a between calculation, the answer is the overlap length divided by the total distribution length. For a left tail calculation, the answer is the cumulative probability at the selected value. For a right tail calculation, the answer is one minus the cumulative probability. A single exact value has probability zero in a continuous model.
Accuracy Notes
The calculator clips interval requests to the valid distribution range. This prevents impossible negative probabilities. It also accepts reversed interval inputs and sorts them before calculation. Decimal control helps you prepare rounded answers for homework, reports, or quick checks.
Export Options
Use CSV export when you need spreadsheet data. Use PDF export when you need a clean summary. Both exports include key inputs, probability results, and distribution measures. These options make the calculator useful for repeated practice and documentation.
Best Practice
Always confirm the lower bound is smaller than the upper bound. Choose the probability type that matches your question. Review the formula section before using exported results. This habit reduces mistakes and improves statistical understanding. Save examples to compare future probability questions with confidence.