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# Normal Distribution CDF Calculator

Calculates the normal distribution cumulative distribution function.  The cumulative normal distribution function describes probabilities for a random variable to fall in the intervals of the form (−∞, x].

### See the Statistical Distributions Overview page for more statistical distribution calculators.

Formula: normdist(x, mn, sd, 1)

## Example 1

If the mean speed of the vehicles on a road is 60 and the standard deviation is 4, what percent are going under 65?

Value Keystrokes Display Description
65 x 65.0000 Stores the x value.
60 μ 60.0000 Stores the mn (mean) value.
4 σ 4.0000 Stores the sd (standard deviation) value.
cdf .8944 Calculates the cumulative distribution function.

## Example 2, Inverse

What speed are 0.95 of the vehicles going under?

These keystrokes assume the values from example 1.

Value Keystrokes Display Description
.95 cdf .9500 Stores the cdf value.
x 66.58 Calculates the x (inverse) value.

## Example 3, solve for a standard deviation

If .95 of the vehicles are going under 65, what would the standard deviation be?

These keystrokes assume the values from example 1.

Value Keystrokes Display Description
.95 cdf .9500 Stores the cdf value.
σ 3.0398 Calculates the sd value.

To calculate the standard values found in tables, use μ = 0 and σ = 1.

Reference:

Normal distribution - Wikipedia