Normal Distribution Probability Calculator
P(X<x), P(X>x) and P(a<X<b) for a normal distribution.
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ⓘ Live results
Results
- P(X < x)
- 90.879%
- P(X > x)
- 9.121%
- z-score
- 1.3333
Quick answer
Probabilities under a normal distribution are found by converting to a z-score and applying the cumulative normal distribution function.
z = (x-μ)/σ, P(X<x) = Φ(z)
How to use the Normal Distribution Probability Calculator
- 1Enter the population mean and standard deviation.
- 2Enter the value x you want a probability for.
- 3The value is converted to a z-score and mapped to a cumulative probability.
Worked example
Using the values the calculator loads with:
Inputs
- Mean μ100
- Standard deviation σ15
- Value x120
Results
- P(X < x)90.879%
- P(X > x)9.121%
- z-score1.3333
Frequently asked questions
What is P(X<x)?
The probability that a randomly drawn value from this distribution is less than x.
How do I find P(a<X<b)?
Compute P(X<b) and P(X<a) separately, then subtract.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.