1. What is a Z-Score Critical Value?

A Z-score critical value is the point on the standard normal distribution that corresponds to a given probability. It represents how many standard deviations away from the mean a particular value lies.

2. How Does the Calculator Work?

The calculator uses the inverse normal distribution function:

Where:

• \( Z \) — Standard score (dimensionless)
• \( p \) — Probability (fraction between 0 and 1)
• \( \text{invNorm} \) — Inverse standard normal distribution function

Explanation: The function finds the Z-score where the cumulative probability equals the input probability.

3. Importance of Z-Score Calculation

Details: Critical Z-scores are essential in hypothesis testing, confidence interval construction, and determining statistical significance in research studies.

4. Using the Calculator

Tips: Enter a probability value between 0 and 1 (exclusive). For example, enter 0.95 for a 95% confidence level.

5. Frequently Asked Questions (FAQ)

Q1: What's the Z-score for 95% confidence?
A: Approximately ±1.96 (two-tailed) or 1.645 (one-tailed).

Q2: How is this different from a regular Z-score?
A: This is the inverse calculation - finding the Z-score that corresponds to a given probability, rather than finding probability from a Z-score.

Q3: What does a negative Z-score mean?
A: It indicates the value is below the mean of the distribution.

Q4: Can I use this for non-normal distributions?
A: No, this calculator specifically uses the standard normal distribution (μ=0, σ=1).

Q5: What's the most extreme Z-score possible?
A: In theory, Z-scores can range from -∞ to +∞, but in practice, values beyond ±4 are extremely rare.