Normal Approximation to Binomial

Approximate binomial probabilities using the normal distribution.

Binomial Parameters

Number of Trials (n)

Probability of Success (p)

Number of Successes (k or x)

Approximation

Mean (μ)25.0000

Std Dev (σ)3.5355

Z-Score (at x = 25)

0.1414

Using continuity correction (x + 0.5)

About this calculator

Overview

When the sample size n is large, the binomial distribution B(n, p) can be approximated by a normal distribution N(np, npq).

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Pro Tips

Use this when 'n' is too large to compute factorials for the exact binomial formula.

Fun Facts

"Rule of Thumb: Approximation is good if np > 5 and n(1-p) > 5."
"Continuity Correction: Since binomial is discrete and normal is continuous, we adjust x by ±0.5."