Statistics

Normal Approximation Calculator

Approximate a binomial distribution with a normal one.

Parameters Live Compute
Calculated Output
Mean 40
Standard deviation 4.899
Approximation valid? yes
Formula: mean = np; SD = sqrt(np(1-p))
Step-by-Step Breakdown
1. Values used:
2. Number of trials = 100
3. Success probability = 0.4
4.
5. Mean = Number of trials x Success probability = 100 x 0.4 = 40
6. Standard deviation = 4.899
7. Approximation valid? = yes
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For large n, a binomial distribution is well approximated by a normal one.

The math behind it

mean = np, SD = sqrt(np(1-p)). The approximation is good when np and n(1-p) both exceed 10.

Worked Example

n 100, p 0.4 gives mean 40, SD about 4.90.

Frequently Asked Questions

When is it valid?

When both np and n(1-p) are at least 10.

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