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Normal Distribution Point Calculator — result sheet
Calculate a z score, density, and cumulative probability for a point under a normal distribution.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: z=(x−μ)/σ; density=exp(−z²/2)/(σ√(2π)); CDF=Φ(z).
The standardized location, point density, and lower-tail cumulative probability are returned separately.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Value x — minimum -1000000000; maximum 1000000000
- Mean — minimum -1000000000; maximum 1000000000
- Standard deviation — minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Value x | 65 |
| Mean | 50 |
| Standard deviation | 10 |
z =1.5; density ≈0.01295; lower-tail probability ≈0.9332.
Assumptions and limits
- The standard deviation is positive and the normal model describes the supplied variable.
- The cumulative value is a numerical standard-normal approximation.
- Empirical fit, truncation, parameter uncertainty, and tail decision rules are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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