Normal CDF Calculator

How to Use the Normal CDF Calculator?

1. First, enter the lower and upper bound values.
2. Enter the mean (μ) and standard deviation (σ) values.
3. Press the 'Calculate' button.
4. As a result, the tool returns the area (probability) under the normal distribution curve.

What is Normal CDF?

The normal cumulative distribution function (CDF) computes the probability that a random variable follows a normal distribution that is less than or equal to a given value.

How to Calculate?

Let's take an example to understand how normal CDF is calculated.

Example:

Find the probability for a normally distributed variable with a mean of 85 and a standard deviation of 20 falls between 98 and 117.

Solution:

Here,
Lower bound (a) = 98,
Upper bound (b) = 117,
Mean (μ) = 85,
Standard Deviation (σ) = 20.

1. Standardize the Bounds

First, convert the lower and upper bounds into the standard normal distribution using the Z-score formula.

2. Find the Probabilities

Now find the probabilities for the Z-scores (Z_a and Z_b) using the standard normal distribution table or calculator.

3. Calculate the Area (probability)

To compute the area, find the difference between the probability values.

So, the probability P(98 ≤ X ≤ 117) is 0.203047 or 20.30%.