Standard Normal Distribution & Z-Score
Standard Normal Distribution & Z-Score: Evaluates Z = (x - μ) / σ = (85 - 70) / 10 = 1.50 and computes cumulative normal distribution probability.
About this standard normal distribution & z-score
Standard Normal Distribution & Z-Score — browser-based utility.
How this tool works
Calculation and parameter relationship: zScore=(value−mean)/standardDeviation
- Select “Raw JSON / Advanced” and paste the sample input.
- Click “Run locally”.
- Compare “Raw Output Data” with the example; revise inputs when an error is shown.
Worked example
Scenario: Measure a value’s distance from its supplied mean in supplied standard-deviation units.
Sample input:
Processing: Parse the three JSON Number fields, require standardDeviation > 0, then calculate zScore=(value−mean)/standardDeviation.
Illustrative output:
Limits and verification
Parameter domains and units: standardDeviation > 0; [value] = [mean] = [standardDeviation]; [zScore] = 1. Results use binary64 floating-point numbers unless BigInt is stated. Result cards show up to 10 significant digits; raw output retains the serialized value. A null ratio means the model has no meaningful finite value for that ratio; it is not zero.
Examples demonstrate an expected workflow; they do not prove every input or every branch of an external specification. Check important results with an independent source before using them for money, security, compliance, safety, or irreversible file changes.
Browser processing boundary
Tool input is processed by code running in the browser and is not intentionally sent to a CZOA processing API. The page can still request ordinary site assets, analytics, or advertising when those services are enabled. Browser extensions and managed-device software remain outside this tool's control.
Relevant references
These references govern or help explain the format, protocol, or calculation used here. Listing a reference does not claim certification or complete implementation of every optional feature.
Content owner: CZOA Tools · Last reviewed: 2026-09-15 · Review methodology
How to use it
- Select “Raw JSON / Advanced” and paste the sample input.
- Click “Run locally”.
- Compare “Raw Output Data” with the example; revise inputs when an error is shown.
Frequently asked questions
How does this Z-score calculator compute its result?+
It parses value, mean, and standardDeviation from the JSON input, rejects a standard deviation of zero or less, and returns zScore as (value − mean) / standardDeviation together with the three supplied values.
Which inputs and controls does the Z-score calculator provide?+
The page offers Value, Mean, and Standard Deviation fields in its interactive form, plus Raw JSON / Advanced input. In the raw mode, enter {"value":85,"mean":70,"standardDeviation":10} and run the calculation locally.
What precision and interpretation limits apply to this Z-score result?+
All four fields are JavaScript Number values, so arithmetic follows binary64 floating-point behavior. The tool standardizes only against the mean and positive standard deviation you supply; it does not test normality or calculate a probability, percentile, or confidence interval.
What result does the worked example produce?+
In the worked example, the tool example supplied {"value":85,"mean":70,"standardDeviation":10} and returned value 85, mean 70, standardDeviation 10, and zScore 1.5 exactly. This verifies that local calculation path and result for that vector, not a statistical inference beyond it.