If ~X is binomially distributed random variable with number parameter ~n, and probability parameter &theta.
~X _ ~ _ B ( ~n , &theta. ) , _ _ p ( ~x ) _ = _ b ( ~x ; ~n , &theta. ) _ = _ comb{~n,~x} &theta.^~x ( 1 - &theta. )^{~n - ~x}
~X _ has mean ~n &theta. , and variance ~n &theta. ( 1 - &theta. ).
If ~n is very large, ~X is approximately normally distributed, with the same mean and variance, i.e.
p ( ~y =< ~x ) _ ~~ _ &Phi.rndb{fract{~x - ~n &theta.,&sqrt.${~n &theta. ( 1 - &theta. )}}}
where &Phi. is the distribution function of the standard normal distribution .