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. |
So, about 89%
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