GCD & LCM Calculator
About Z-Score Calculator
The Standard Normal Z-Score & P-Value Calculator computes standard deviations from the mean ($Z = \frac{X - \mu}{\sigma}$), two-tailed/one-tailed $p$-values, normal curve percentiles, and inverse raw scores ($X = \mu + Z\sigma$).
How to Use Z-Score Calculator
Step 1
Enter Raw Value ($X$), Mean ($\\mu$), and Standard Deviation ($\\sigma$).
Step 2
Click "Calculate Z-Score".
Step 3
Review computed Z-score, percentile ranking, and normal curve area.
Step 4
Click "Copy Result".
Practical Use Cases for Z-Score Calculator
Standardized Test Scoring (SAT, ACT, GRE, IQ)
Convert raw test scores into Z-scores and percentile ranks relative to national bell curve norms.
Hypothesis Testing & Statistical Anomaly Detection
Identify statistical outlier data points falling beyond $|Z| > 3.0$ standard deviations in quality control.
Input & Output Examples
Calculating Z-Score for Raw Score 85 (Mean 70, Std Dev 10)
Raw Score (X): 85, Mean ($\mu$): 70, Std Dev ($\sigma$): 10
Z-Score: +1.50 | Percentile: 93.32% ($p = 0.0668$ one-tailed) | Normal Curve Area: Above Average
Key Features & Performance
- ✓Calculates Z-Score from Raw Score ($X$), Mean ($\\mu$), and Standard Deviation ($\\sigma$).
- ✓Inverse mode: compute required Raw Score ($X$) for a target Z-score or Percentile rank.
- ✓Computes Left-tailed $P(Z < z)$, Right-tailed $P(Z > z)$, and Two-tailed $p$-values.
- ✓Interactive normal distribution bell curve diagram with shaded probability regions.
- ✓100% Client-Side calculation.
- ✓1-Click Copy Z-score analysis.
Key Terminology & Definitions
Z-Score (Standard Score)
A dimensionless quantity representing the number of standard deviations a given data point $X$ lies above or below the population mean: $Z = \\frac{X - \\mu}{\\sigma}$.
Cumulative Probability $P(Z < z)$
The total area under the standard normal curve to the left of a given Z-score, representing the percentile rank.