The similarity of the
binomial and
normal distributions is very important. Calculating the chances that a binomial
random variable, with large N, will be less that something around, say, N/2 requires a lot of
calculation.
The normal distribution can be used as a much easier-to-calculate approximation. Set up the variable with mu equaling n*p and sigma-squared equaling n*p*(1-p) and you have an easier way to find your answer. This is considered to be a very good approximation as long as sigma-squared is greater than 10.