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Sampling Distribution Probability Calculator — result sheet
Calculate the probability that a sample mean falls between two bounds under a normal sampling-distribution assumption.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Standard error=population standard deviation/√n; P(lower≤X̄≤upper)=Φ((upper−μ)/SE)−Φ((lower−μ)/SE).
The calculator models the distribution of sample means rather than individual observations and displays the standard-error scaling.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Population mean — minimum -1.0E+15; maximum 1.0E+15
- Population standard deviation — minimum 1.0E-6; maximum 1.0E+15
- Sample size — minimum 1; maximum 1000000000
- Lower mean bound — minimum -1.0E+15; maximum 1.0E+15
- Upper mean bound — minimum -1.0E+15; maximum 1.0E+15
Worked example
| Input | Value |
|---|---|
| Population mean | 100 |
| Population standard deviation | 15 |
| Sample size | 25 |
| Lower mean bound | 95 |
| Upper mean bound | 105 |
Standard error = 3; probability ≈ 0.904.
Assumptions and limits
- The population standard deviation and mean are treated as supplied values.
- The normal sampling-distribution model is appropriate or is being used as an approximation.
- Finite-population corrections, dependence, nonresponse, and estimation error 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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