Normal Model Calculator
Calculate probabilities and quantiles for a normal distribution with given mean and standard deviation.
Published by:
isCalculator Editorial Team
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How to use this tool?
The Normal Model Calculator computes probabilities and quantiles for a normal distribution with your specified mean (μ) and standard deviation (σ).
Step-by-Step Instructions
- Enter Parameters: Fill in the Mean (μ) and Standard Deviation (σ) fields. σ must be positive.
- Provide One Input (choose either):
- X Value: To find the probability P(X ≤ x) (cumulative probability up to that value).
- Probability: A number between 0 and 1 (exclusive) to find the corresponding quantile (x-value).
- Calculate: Click the Calculate button.
- Read Result: The output shows either the probability (if you entered an X value) or the quantile (if you entered a probability), along with a brief explanation.
Note: Enter only one of X Value or Probability at a time. All numeric inputs accept decimals. The calculator uses standard normal distribution formulas (no unit conversion needed).
Previous Results
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Frequently Asked Questions
A normal distribution is a symmetric, bell-shaped probability distribution characterized by its mean (μ) and standard deviation (σ). It is widely used in statistics.
Enter the mean and standard deviation. Then either enter an X value to compute the probability P(X ≤ x) or enter a probability to find the corresponding quantile (x). Click Calculate.
The calculator requires only one of these inputs. If both are entered, an error message will appear. Please clear one field.
