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Binomial Normal Approximation Calculator — result sheet
Estimate an inclusive binomial count probability using a normal approximation with an optional continuity correction.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: μ=np; σ=√(np(1−p)); inclusive count interval uses Φ((upper+0.5−μ)/σ)−Φ((lower−0.5−μ)/σ) when corrected.
The discrete count interval is translated to a continuous normal interval, with the half-unit boundary adjustment exposed as a choice.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Number of trials — minimum 1; maximum 1000000
- Success probability — minimum 0; maximum 1
- Lower inclusive count — minimum 0; maximum 1000000
- Upper inclusive count — minimum 0; maximum 1000000
- Continuity correction — 2 choices
Worked example
| Input | Value |
|---|---|
| Number of trials | 100 |
| Success probability | 0.4 |
| Lower inclusive count | 35 |
| Upper inclusive count | 45 |
| Continuity correction | yes |
Approximate probability for 35–45 successes is about 0.738.
Assumptions and limits
- Trials are independent Bernoulli observations with a constant success probability.
- The result is an approximation and is less reliable when the binomial distribution is highly skewed or sparse.
- The interval is inclusive and clipped to the valid count range conceptually; exact binomial probability is not returned.
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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