1. What is the Standard Normal Value (Z-Score)?

The Z-score (standard score) represents how many standard deviations an element is from the mean. It allows comparison of scores from different normal distributions by standardizing them.

2. How Does the Calculator Work?

The calculator uses the standard normal formula:

Where:

• \( X \) — Raw score/value
• \( \mu \) — Mean of the population
• \( \sigma \) — Standard deviation of the population

Explanation: The formula calculates how many standard deviations a value is above or below the mean.

3. Importance of Z-Score Calculation

Details: Z-scores are crucial in statistics for probability calculations, comparing different data sets, and identifying outliers. They're used in fields like psychology, finance, and quality control.

4. Using the Calculator

Tips: Enter the raw value (X), population mean (μ), and standard deviation (σ). Standard deviation must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What does a Z-score of 0 mean?
A: A Z-score of 0 indicates the value is exactly at the mean.

Q2: What is considered an unusual Z-score?
A: Typically, Z-scores below -2 or above 2 are considered unusual (beyond 2 standard deviations from the mean).

Q3: Can Z-scores be negative?
A: Yes, negative Z-scores indicate values below the mean.

Q4: What's the relationship between Z-scores and percentiles?
A: Z-scores can be converted to percentiles using standard normal distribution tables or functions.

Q5: When should I use this calculation?
A: Use it when you need to standardize values for comparison or when working with normally distributed data.