# How do you read a cumulative binomial probability table?

Nov 26, 2017

Cumulative binomial probability tables give are used to find $P \left(X \le x\right)$for the distribution X~B(n,p)

Using some basic rules you can work out many different probabilities of a binomial distribution:
$P \left(X < x\right) = P \left(X \le x - 1\right)$
$P \left(X \ge x\right) = 1 - P \left(X \le x - 1\right)$
$P \left(X > x\right) = 1 - P \left(X \le x\right)$
$P \left(A < X \le B\right) = P \left(X \le B\right) - P \left(X \le A\right)$
... and so on.

There is a seperate table for each sample size ("$n$") so first find the correct table of $n$=your sample size.

Then find the column on that table with the probability "$p$" of your distribution. The the number in the row $x = a$ is $P \left(X \le a\right)$

ie. to find $P \left(4 \le X \le 9\right)$ for the the distribution X~B(14, 0.55), go to the table for $n = 14$. Then find the column $p = 0.55$. Look for the row $x = 9$ in that column, which gives 0.8328, and then look for $x = 3$ in that column, which gives 0.0114.
So $P \left(4 \le X \le 9\right) = 0.8328 - 0.0114 = 0.8214$