# Normal Approximation Calculator

The normal distribution is used as an approximation for the Binomial Distribution when X ~ B(n, p) and if 'n' is large and/or p is close to 1/2, then X is approximately N(np, npq). Binomial distribution is most often used to measure the number of successes in a sample of size 'n' with replacement from a population of size N. It is used as a basis for the binomial test of statistical significance. Find the Probability, Mean and Standard deviation using this normal approximation calculator.

## Normal Approximation to the Binomial Distribution

Code to add this calci to your website

#### Formula:

q = 1 - p
M = N x p
SD = √(M x q)
Z Score = (x - M) / SD
Z Value = (x - M - 0.5)/ SD
**Where,**
N = Number of Occurrences
p = Probability of Success
x = Number of Success
q = Probability of Failure
M = Mean
SD = Standard Deviation
### Example:

Find the normal approximation for an event with number of occurences as 10, Probability of Success as 0.7 and Number of Success as 7.

#### Solution:

Probability of Failure = 1 - 0.7 = 0.3

Mean = 10 x 0.7 = 7

Standard Deviation = √(7 x 0.3) = 1.4491

Z Score = (7 - 7) / 1.4491 = 0

Z Value = (7 - 7 - 0.5) / 1.4491

= -0.345