1. What is the Normal Distribution CDF?

The Normal Distribution Cumulative Distribution Function (CDF) gives the probability that a normally distributed random variable will be less than or equal to a given value. It's fundamental in statistics for probability calculations.

2. How Does the Calculator Work?

The calculator uses the standard normal CDF formula:

Where:

• \( x \) — The value at which to evaluate the CDF
• \( \mu \) — Mean of the distribution
• \( \sigma \) — Standard deviation of the distribution
• \( \text{erf} \) — The Gauss error function

Explanation: The formula converts the input to a z-score, then calculates the area under the normal curve up to that point.

3. Importance of Normal CDF Calculation

Details: The normal CDF is essential for statistical hypothesis testing, confidence intervals, and probability calculations in normally distributed data.

4. Using the Calculator

Tips: Enter your value (x), the mean (μ) and standard deviation (σ) of your normal distribution. Standard deviation must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What does the CDF value represent?
A: The CDF value represents the probability that a random variable from this distribution will be less than or equal to your input value x.

Q2: How accurate is this calculation?
A: The calculator uses a numerical approximation of the erf function accurate to about 7 decimal places.

Q3: What's the difference between PDF and CDF?
A: The PDF gives the probability density at a point, while the CDF gives the cumulative probability up to that point.

Q4: Can I use this for standard normal distribution?
A: Yes, set μ=0 and σ=1 for standard normal distribution calculations.

Q5: What if my standard deviation is very small?
A: Extremely small σ values may lead to numerical instability in the calculation.