Normal Distribution Calculator
Calculate probabilities and z-scores for normal distribution. Enter the mean, standard deviation, and x-value to determine the cumulative probability, probability density, and standardized z-score.
How to Use
- Mean (μ): Enter the average or expected value of your distribution
- Standard Deviation (σ): Enter the measure of spread in your data (must be positive)
- X Value: Enter the specific value for which you want to calculate probabilities
- Click "Calculate" to see the z-score and probability results
Understanding the Results
- Z-Score: Shows how many standard deviations the x-value is from the mean
- Cumulative Probability P(X ≤ x): The probability that a random value is less than or equal to your x-value
- Probability Density: The height of the normal distribution curve at your x-value
- P(X > x): The probability that a random value is greater than your x-value
About Normal Distribution
The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that is symmetric about the mean. It is one of the most important probability distributions in statistics and appears naturally in many real-world phenomena.
The standard normal distribution has a mean of 0 and a standard deviation of 1. Any normal distribution can be converted to the standard normal distribution using z-scores.