Normal CDF Lower Calculator
Introduction & Importance
The Normal Cumulative Distribution Function (CDF) Lower is a crucial statistical tool used to determine the probability that a random variable is less than a given value. It’s widely used in various fields, including finance, engineering, and science.
How to Use This Calculator
- Enter the value of X, Mu (mean), and Sigma (standard deviation).
- Click ‘Calculate’.
- View the result and chart below.
Formula & Methodology
The formula for Normal CDF Lower is:
P(X < x) = 0.5 * (1 + erf(x / (2 * sqrt(2))))
Real-World Examples
Example 1
X = 1, Mu = 0, Sigma = 1. The result is 0.158655254.
Example 2
X = 2, Mu = 1, Sigma = 2. The result is 0.022750132.
Example 3
X = -1, Mu = 0, Sigma = 1. The result is 0.841344746.
Data & Statistics
| X | Mu | Sigma | Result |
|---|---|---|---|
| 1 | 0 | 1 | 0.158655254 |
| 2 | 1 | 2 | 0.022750132 |
| -1 | 0 | 1 | 0.841344746 |
| X | Mu | Sigma | Result |
|---|---|---|---|
| 0 | 0 | 1 | 0.5 |
| 1 | 1 | 1 | 0.841344746 |
| 2 | 2 | 2 | 0.977249868 |
Expert Tips
- Understand the difference between Normal CDF Lower and Normal CDF.
- Always use the correct values for Mu and Sigma.
- For more accurate results, use a larger number of decimal places.
Interactive FAQ
What is the difference between Normal CDF and Normal CDF Lower?
Normal CDF gives the probability that a random variable is less than or equal to a given value, while Normal CDF Lower gives the probability that a random variable is less than a given value.
How does this calculator work?
It uses the formula for Normal CDF Lower and calculates the result based on the inputs provided.
For more information, see the following authoritative sources: