# Probability distribution explorer

> Plot common distributions and selected tail probabilities.

[Open tool](https://www.toolcabana.com/su/probability-distribution-explorer) · [Statistics and analysis](https://www.toolcabana.com/su/category/statistics-and-analysis)

Tool ID: probability-distribution-explorer. Requested language: su. Description language: en. Complete guide translation: no; untranslated sections use English.

## Overview (en)

The Probability distribution explorer plots a normal, binomial or Poisson distribution and returns tail probabilities at a threshold x you choose. For the normal distribution it reports P(X ≤ x) and P(X > x) with an 81-point density table. For binomial, up to 500 trials, and Poisson it lists the probability of each count and the cumulative P(X ≤ floor(x)).

## Supported tasks (en)

Plot common distributions and selected tail probabilities.

## Steps (en)

1. Enter the requested values in the settings panel.
2. Set distribution, normal mean / poisson rate, normal standard deviation, binomial trials, binomial success probability and the other available options.
3. Run probability distribution explorer, review the output, then use the available copy or download controls.

## Settings

- Distribution (en; key: distribution; type: select): normal [en], binomial [en], poisson [en]
- Normal mean / Poisson rate (en; key: mean; type: number); minimum: -1000000; maximum: 1000000
- Normal standard deviation (en; key: sd; type: number); minimum: 0.000001; maximum: 1000000000000
- Binomial trials (en; key: trials; type: number); minimum: 1; maximum: 500
- Binomial success probability (en; key: probability; type: number); minimum: 0; maximum: 1
- Threshold x (en; key: x; type: number); minimum: -1000000; maximum: 1000000

## Limitations (en)

Local bounded calculations. Numeric inputs must be finite and within the visible ranges. Lists and tables have operation-specific limits. Models, estimates and supplied rates must be checked against your intended use.

## Privacy and connections (en)

This operation processes its source in your browser. Copy and download are explicit actions; source input is not saved in an account or history.

## Questions (en)

### How do I find the probability that a normal value is below a threshold?

Choose normal, enter the mean, standard deviation and threshold x. The explorer standardizes x as (x − mean) / sd and returns P(X ≤ x) and P(X > x). With mean 0, sd 1 and x = 1, P(X ≤ x) is about 0.841.

### How is the binomial probability table calculated?

For n trials and success probability p, each count k from 0 to n gets the probability C(n, k) × p^k × (1 − p)^(n − k), computed with logarithms for stability. The cumulative result sums all k up to the floor of the threshold x. Trials can range from 1 to 500.

### Which field sets the Poisson rate?

The Poisson distribution uses the Normal mean / Poisson rate field as its average count, from 0 to 200. The table lists P(X = k) from k = 0 well past the mean, and the result gives P(X ≤ floor(x)) for your threshold.

### Where is my input processed?

This operation processes its source in your browser. Copy and download are explicit actions; source input is not saved in an account or history.

### What are the input limits?

Local bounded calculations. Numeric inputs must be finite and within the visible ranges. Lists and tables have operation-specific limits. Models, estimates and supplied rates must be checked against your intended use.

## Related tools

- [Descriptive statistics calculator](https://www.toolcabana.com/su/descriptive-statistics-calculator)
- [Linear regression calculator](https://www.toolcabana.com/su/linear-regression-calculator)
- [Confidence interval calculator](https://www.toolcabana.com/su/confidence-interval-calculator)
- [Sample size calculator](https://www.toolcabana.com/su/sample-size-calculator)