A cumulative binomial table is used in statistics to calculate the probability that the value of a random variable falls within a specific range. Often used to solve binomial distribution problems, cumulative binomial tables usually refer to the probability that the value of the random variable is less than or equal to a specified value.
The easiest way to solve one type of binomial distribution problem is to look up the answer in a cumulative binomial table. Further, a cumulative binomial table isn’t just one table. It’s actually multiple tables that allow you to look up each value for the random variable in your problem. For example, in a coin-toss experiment using two coins, the problem asks what the probability is of getting one or fewer heads. The resulting cumulative binomial table lists all values for the probability that a toss results in no heads in addition to the probability that a toss results in one head. Unfortunately, a cumulative binomial table may not always give the answer necessary if, for instance, you want to find a specific value – not one that's less than or equal to it. For solving these kinds of problems, using the binomial formula is quicker.