1. What is the Standard Normal Value?

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

2. How Does the Calculator Work?

The calculator uses the standard normal formula:

Where:

• \( X \) — The value to be standardized
• \( \mu \) — The mean of the distribution (default 0)
• \( \sigma \) — The standard deviation of the distribution (default 1)

Explanation: The formula converts any normal distribution to the standard normal distribution with mean 0 and standard deviation 1.

3. Importance of Z-Score Calculation

Details: Z-scores are crucial in statistics for probability calculations, hypothesis testing, and comparing results from different normal distributions.

4. Using the Calculator

Tips: Enter your value (X), the mean (μ), and 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 (about 5% of values in a normal distribution).

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

Q4: How are Z-scores used in real life?
A: They're used in standardized testing, quality control, medical measurements, and financial risk assessment.

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