1. What is Normal Distribution?

The normal distribution, also known as Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

2. How Does the Z-Score Calculator Work?

The calculator uses the Z-score formula:

Where:

• \( Z \) — Standard score (how many standard deviations from the mean)
• \( X \) — Raw score to be standardized
• \( \mu \) — Mean of the population
• \( \sigma \) — Standard deviation of the population

Explanation: The Z-score tells you how far a value is from the mean in terms of standard deviations. Positive Z-scores are above the mean, negative are below.

3. Importance of Z-Score Calculation

Details: Z-scores are crucial for comparing values from different normal distributions, identifying outliers, and calculating probabilities in statistics.

4. Using the Calculator

Tips: Enter the raw score (X), population mean (μ), and population standard deviation (σ). Standard deviation must be greater than 0.

5. Frequently Asked Questions (FAQ)

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

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 used with non-normal distributions?
A: While you can calculate Z-scores for any distribution, they are most meaningful for normal distributions.

Q4: How do I interpret a negative Z-score?
A: A negative Z-score means the value is below the mean of the distribution.

Q5: What's the relationship between Z-scores and percentiles?
A: Z-scores can be converted to percentiles using standard normal distribution tables or functions.