1. What is the Inverse Normal Function?

The inverse normal function, invNorm(area), calculates the z-score corresponding to a given cumulative probability (area) under the standard normal curve. This is a fundamental concept in A-level statistics.

2. How Does the Calculator Work?

The calculator uses the inverse standard normal distribution function:

Where:

• \( Z \) — Standard normal deviate (z-score)
• \( area \) — Cumulative probability (0 < area < 1)

Explanation: The function returns the z-score where the area under the standard normal curve to the left of z equals the input probability.

3. Importance of Z-scores

Details: Z-scores are essential in hypothesis testing, confidence intervals, and standardization of data. They indicate how many standard deviations an element is from the mean.

4. Using the Calculator

Tips: Enter a probability value between 0 and 1 (exclusive). For example, to find the z-score for the 95th percentile, enter 0.95.

5. Frequently Asked Questions (FAQ)

Q1: What does a z-score of 1.96 represent?
A: A z-score of 1.96 corresponds to the 97.5th percentile, commonly used for 95% confidence intervals.

Q2: How is this different from normal CDF?
A: Normal CDF gives probability from z-score, while inverse normal gives z-score from probability.

Q3: What's the z-score for the median?
A: The median corresponds to a z-score of 0 (50th percentile).

Q4: Can I use this for non-standard normal distributions?
A: For non-standard distributions, convert using \( X = \mu + Z\sigma \) after finding Z.

Q5: Why can't I enter 0 or 1?
A: The standard normal distribution approaches but never reaches these extremes.