Normal Approximation Calculator

Approximate a binomial distribution with a normal one.

Mean 40

Standard deviation 4.899

Approximation valid? yes

Formula: mean = np; SD = sqrt(np(1-p))

Step-by-step with your numbers:

1. Values used:

2. Number of trials = 100

3. Success probability = 0.4

5. Mean = Number of trials x Success probability = 100 x 0.4 = 40

6. Standard deviation = 4.899

7. Approximation valid? = yes

Did we solve your problem today?

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.

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

When is it valid?

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