Free Normal Distribution Probability Calculator
Probability that X falls below, above or between values.
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Result
P(X < x)
93.319%
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Short answer
Probability that X falls below, above or between values.
What is the Normal Distribution Probability Calculator?
Probability that X falls below, above or between values.
How does the Normal Distribution Probability Calculator work?
Enter the inputs above and read the result.
Formula
Variables
ΦStandard normal cumulative distribution function
Explanation
Converting to a z-score lets any normal distribution be evaluated using the standard normal curve.
Examples
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Advantages
Limitations
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Tips
Related concepts
The Normal Distribution Probability Calculator sits inside the Math Calculators hub, in the statistics & probability cluster. Describing data and quantifying uncertainty. Understanding the terms below makes the output easier to interpret and easier to compare against neighbouring measures.
Practical use cases and industry applications
Understanding Normal Distribution Probability
Probability that X falls below, above or between values. Within math calculators, normal distribution probability belongs to the statistics & probability cluster, where it shares terminology and assumptions with closely related tools.
Learning how normal distribution probability is calculated
Converting to a z-score lets any normal distribution be evaluated using the standard normal curve. Working through the variables one at a time — Φ — makes the result reproducible by hand and easier to sanity-check.
Using normal distribution probability to make a decision
Because outputs depend on the assumptions you enter, run more than one scenario before committing to a figure.
How normal distribution probability compares with related measures
distribution, dispersion, significance, sample all describe adjacent aspects of statistics & probability. Comparing this calculator's output against those measures — using the related tools listed on this page — prevents a single metric from being read in isolation.
Frequently asked questions
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