Cumulative Distribution Calculator
Calculate the cumulative probability of a normal distribution at a chosen x value, using a mean and standard deviation.
Formula:
P(X ≤ x) = Φ(z), where z = (x − μ) / σ
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Privacy: calculations run locally in your browser. No inputs are stored or transmitted.
How it works
This page computes the normal cumulative distribution function, which gives the probability that a normally distributed variable is less than or equal to x.
Example interpretation: if the result is 0.6915, then about 69.15% of values are expected to be at or below x.
Examples
- x = 70, μ = 65, σ = 10
- The result is the probability mass to the left of x on the normal curve.
FAQ
- What does this cumulative distribution calculator compute?
It computes the normal cumulative probability P(X ≤ x) for a chosen x, mean, and standard deviation.
- What is a cumulative distribution value?
A cumulative distribution value is the probability that a random variable is less than or equal to a specified value.
- What formula is used?
This page uses the normal CDF based on the error function: Φ(z) = 0.5 × (1 + erf(z / √2)).
- Why must standard deviation be positive?
Because the z score and normal CDF require division by the standard deviation.
- Are calculations stored?
No. Everything runs locally in your browser.