1. What is the Standard Normal Value?

The standard normal value (Z-score) measures how many standard deviations an element is from the mean. It's used in statistics to compare different normal distributions and calculate probabilities.

2. How Does the Calculator Work?

The calculator uses the standard normal formula:

Where:

• \( X \) — The value being standardized
• \( \mu \) — Mean of the distribution (default 0)
• \( \sigma \) — Standard deviation of the distribution (default 1)

Explanation: The formula transforms any normal distribution to the standard normal distribution (μ=0, σ=1) for comparison and probability calculation.

3. Importance of Z-Score Calculation

Details: Z-scores are essential for hypothesis testing, confidence intervals, and determining percentiles in normal distributions. They allow comparison across different scales and measurements.

4. Using the Calculator

Tips: Enter your raw score (X), population mean (μ), and standard deviation (σ). For standard normal distribution, use μ=0 and σ=1. Standard deviation must be positive.

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: How do I interpret positive and negative Z-scores?
A: Positive Z-scores indicate values above the mean, negative scores indicate values below the mean.

Q3: What's the range of possible Z-scores?
A: In theory, Z-scores can range from -∞ to +∞, but in practice most values fall between -3 and +3.

Q4: How is this related to TI-84 calculators?
A: This uses the same formula as TI-84's normal distribution functions (normalcdf, invNorm).

Q5: Can I calculate probabilities from Z-scores?
A: Yes, using standard normal distribution tables or calculator functions that give the area under the curve.