Z-Score Calculator
Calculate z-scores and probabilities
Distribution Parameters
Results
1.000
Z-Score
Percentile84.1%
Position relative to the population
Probability0.841
Probability of value being less than or equal
InterpretationWithin two standard deviations (somewhat unusual)
Statistical significance
Confidence Intervals:
68% Confidence Interval
65.0 to 75.0
95% Confidence Interval
60.0 to 80.0
99% Confidence Interval
55.0 to 85.0
Understanding Z-Scores
What is a Z-Score?
A z-score (or standard score) indicates how many standard deviations away from the mean a data point is. It allows comparison of values from different normal distributions by standardizing them to a common scale.
Interpretation
- • Z = 0: Value equals the mean
- • Z > 0: Value is above the mean
- • Z < 0: Value is below the mean
- • |Z| = 1: One standard deviation from mean
Normal Distribution Properties
68-95-99.7 Rule
- • 68% within ±1σ
- • 95% within ±2σ
- • 99.7% within ±3σ
Common Z-Scores
- • Z = ±1.645: 90% confidence
- • Z = ±1.96: 95% confidence
- • Z = ±2.576: 99% confidence
Applications
- • Statistical testing
- • Quality control
- • Educational scoring
- • Research analysis