1. What is Inverse Normal Probability?

The inverse normal probability function calculates the z-score corresponding to a given cumulative probability in a standard normal distribution. It is the inverse operation of the normal cumulative distribution function.

2. How Does the Calculator Work?

The calculator uses the inverse normal probability formula:

Where:

• \( p \) — Cumulative probability (0 ≤ p ≤ 1)
• \( z \) — Z-score corresponding to the probability

Explanation: The function returns the z-value such that the area under the standard normal curve to the left of z equals the given probability p.

3. Importance of Z-Score Calculation

Details: Inverse normal calculations are essential in statistics for hypothesis testing, confidence intervals, and determining critical values in various statistical analyses.

4. Using the Calculator

Tips: Enter a probability value between 0 and 1. The calculator will return the corresponding z-score from the standard normal distribution.

5. Frequently Asked Questions (FAQ)

Q1: What is a z-score?
A: A z-score represents how many standard deviations a data point is from the mean of a normal distribution.

Q2: What does invNorm(0.95) represent?
A: invNorm(0.95) returns the z-score where 95% of the area under the normal curve lies to the left of that z-value.

Q3: When is inverse normal probability used?
A: It's used in statistical testing, quality control, risk assessment, and any application requiring determination of threshold values based on probabilities.

Q4: Are there limitations to inverse normal calculations?
A: The calculation assumes a perfect normal distribution, which may not always reflect real-world data distributions accurately.

Q5: What's the relationship between p-values and z-scores?
A: Z-scores can be converted to p-values and vice versa using the normal distribution function and its inverse.