📊Probability Distribution Calculator

Calculate normal and binomial probability distributions.

Mean (μ)

Standard Deviation (σ)

Bell Curve Visualization

Sigma Range Probabilities

1σ Range

-1.00 to 1.00

68.2689%

2σ Range

-2.00 to 2.00

95.4500%

3σ Range

-3.00 to 3.00

99.7300%

Variance (σ²)

1.0000

Peak PDF Value

0.398942

P(X ≤ μ)

50.0000%

About Probability Distribution Calculator

Calculate probabilities for normal and binomial distributions with step-by-step results and visual probability curves. Enter your distribution parameters and instantly compute probability values, cumulative probabilities, and find Z-scores for normal distributions. Essential for statistics courses, data science, and any field that involves probability calculations.

How to Use Probability Distribution Calculator

1
Step 1
Select the distribution type (normal, binomial, or Poisson) and enter the required parameters.
2
Step 2
Enter the value or range you want to compute the probability for.
3
Step 3
View the probability result, Z-score (for normal), and a visual probability curve.

Common Use Cases

Statistics students calculating normal distribution probabilities for coursework
Data scientists verifying probability calculations in analysis workflows
Researchers computing confidence intervals and hypothesis testing p-values
Quality control engineers applying statistical distributions to process variation

Frequently Asked Questions

What distributions does the calculator support?

The calculator handles Normal distribution (with Z-score computation and standard deviation), Binomial distribution (n trials, p probability), and Poisson distribution calculations.

Can I calculate P(X < a), P(X > a), and P(a < X < b)?

Yes. For normal distributions, you can calculate left-tail, right-tail, and two-tail probabilities for any value range.

What is a Z-score?

A Z-score measures how many standard deviations a value is from the mean. It is calculated as Z = (X - μ) / σ and used to find probabilities in a standard normal distribution table.