Binomial Distribution

Parameters: Probability of success in each trial (p), Number of total trials (n)

Formula:

Formula for binomial distribution

for i = 0,1,2,...n; p is greater than 0; 0 is less than n is less than 1,000

where:

Formula for binomial distribution

and x = number of successful trials

Method: Direct Simulation

Comment: Computation time increases linearly with number of trials.

Note:

Crystal Ball limits n to 1,000, partly for performance reasons and partly because a binomial distribution with a large n can be approximated with Poisson and normal distributions. The Poisson approximation should be used when n^0.31*(1-p) is less than 0.47, and the normal approximation should be used when n^0.31*(1-p) is greater than 0.47.