Normal Distribution Calculator
Calculate probabilities for the normal (Gaussian) distribution.
Find the probability between, above, or below any value given the mean and standard deviation.
Normal Distribution Probability
Normal Distribution (Bell Curve):
The normal distribution is the most important probability distribution in statistics. It is defined by two parameters: the mean (μ) and the standard deviation (σ).
Probability Density Function:
f(x) = (1 / (σ√(2π))) × e^(-(x-μ)²/(2σ²))
Key properties:
- Symmetric around the mean
- Mean = median = mode
- 68.27% of data within ±1σ
- 95.45% of data within ±2σ
- 99.73% of data within ±3σ
Standard Normal: When μ = 0 and σ = 1, it is the standard normal distribution. Any normal distribution can be converted to standard normal using z-scores.