Normal Distribution Calculator
Calculate probabilities for normal (Gaussian) distribution. Find P(X ≤ x), P(X ≥ x), or P(x₁ ≤ X ≤ x₂) with z-scores and percentiles.
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Average or center of the distribution
Spread or variability of the distribution
Value to calculate probability for
How to Use Normal Distribution Calculator
- 1
Enter the mean (μ) of the distribution.
- 2
Enter the standard deviation (σ).
- 3
Choose calculation type (less than, greater than, or between).
- 4
Enter the value(s) to calculate probability for.
Frequently Asked Questions
What is normal distribution?▾
Normal distribution is a bell-shaped probability distribution that is symmetric around the mean. Many natural phenomena follow this pattern, including heights, test scores, and measurement errors.
What is the 68-95-99.7 rule?▾
About 68% of data falls within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.
When to use normal distribution?▾
Use when data is continuously distributed, symmetric, and bell-shaped. Common applications include IQ scores (μ=100, σ=15), SAT scores (μ=500, σ=100), and many natural measurements.
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