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.
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.
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