Normal Distribution Generator
Generate random numbers that follow a normal (Gaussian) distribution with your specified mean and standard deviation. Perfect for simulations, testing statistical methods, or generating realistic synthetic data.
What is the Normal Distribution?
The normal distribution, also known as the Gaussian distribution or bell curve, is one of the most important probability distributions in statistics. Many natural phenomena follow this distribution, including:
- Heights and weights in a population
- Measurement errors
- Test scores
- Blood pressure readings
- Manufacturing tolerances
Parameters
- Mean (μ): The center of the distribution. The peak of the bell curve occurs at this value.
- Standard Deviation (σ): Controls the spread of the distribution. About 68% of values fall within ±1 standard deviation of the mean, 95% within ±2, and 99.7% within ±3.
The Empirical Rule
| Range | Percentage of Data |
|---|---|
| μ ± 1σ | 68.27% |
| μ ± 2σ | 95.45% |
| μ ± 3σ | 99.73% |
Applications
- Simulations: Generate realistic data for testing statistical methods
- Education: Create practice datasets for students
- Research: Generate synthetic data with known properties
- Monte Carlo Methods: Simulate complex systems and processes
Algorithm
This generator uses the Box-Muller transform, a method for generating pairs of independent standard normally distributed random numbers from uniformly distributed random numbers.