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# Normal Approximation Calculator

Find the Probability, Mean and Standard deviation using this normal approximation calculator. Just enter the number of occurrences, the probability of success, and number of success.

## Normal Approximation to the Binomial Distribution

Find the Probability, Mean and Standard deviation using this normal approximation calculator. Just enter the number of occurrences, the probability of success, and number of success.

#### 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

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 ½, 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.

Use this online binomial distribution normal approximation calculator to simplify your calculation work by avoiding complexities.

### 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