1. What is Z-Score to Probability Conversion?

Z-Score to Probability conversion calculates the probability that a standard normal random variable is less than or equal to a given z-score. This conversion is fundamental in statistics for determining p-values and confidence intervals.

2. How Does the Calculator Work?

The calculator uses the standard normal cumulative distribution function:

Where:

• \( P \) — Probability value
• \( z \) — Z-score value
• \( \Phi(z) \) — Cumulative distribution function of the standard normal distribution

Explanation: The calculator numerically approximates the integral of the standard normal distribution to convert z-scores to corresponding probability values.

3. Importance of Probability Calculation

Details: Accurate probability calculation from z-scores is essential for statistical hypothesis testing, determining significance levels, and interpreting standard normal distribution results in various research and analytical applications.

4. Using the Calculator

Tips: Enter the z-score value (positive or negative). The calculator will compute the corresponding probability value expressed as a percentage.

5. Frequently Asked Questions (FAQ)

Q1: What is a z-score?
A: A z-score measures how many standard deviations an element is from the mean of a distribution.

Q2: What does the probability value represent?
A: The probability value represents the likelihood that a randomly selected score from the distribution will be less than or equal to the given z-score.

Q3: How are z-scores and probabilities related?
A: Z-scores and probabilities are related through the cumulative distribution function of the standard normal distribution.

Q4: What is the range of possible probability values?
A: Probability values range from 0% to 100%, corresponding to z-scores from -∞ to +∞.

Q5: When is this conversion typically used?
A: This conversion is commonly used in statistical testing, quality control, risk assessment, and various scientific research applications.