1. What is the 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:

• \( X \) — The value being standardized
• \( \mu \) — The mean of the population
• \( \sigma \) — The standard deviation of the population

Explanation: The Z-score measures how many standard deviations an element is from the mean. A Z-score of 0 indicates the value is exactly at the mean.

3. Importance of Z-score Calculation

Details: Z-scores are crucial in statistics for comparing data points from different normal distributions, identifying outliers, and standardizing scores for comparison across different datasets.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What does a positive Z-score mean?
A: A positive Z-score indicates the data point is above the mean.

Q2: What does a negative Z-score mean?
A: A negative Z-score indicates the data point is below the mean.

Q3: How is Z-score used in hypothesis testing?
A: Z-scores are used to determine how far a data point is from the mean in terms of standard deviations, which helps in calculating p-values and making decisions in hypothesis testing.

Q4: What is considered an extreme Z-score?
A: Typically, Z-scores beyond ±2 are considered unusual, and beyond ±3 are considered extreme outliers.

Q5: Can Z-scores be used for non-normal distributions?
A: While Z-scores can be calculated for any distribution, their interpretation is most meaningful for normal distributions.