## Using Binomial Distribution Tables

Th binomial distribution is discrete. This means that if a random variable  {jatex options:inline}X{/jatex}  follows a binomial distribution  {jatex options:inline}B(n,p){/jatex}  and  {jatex options:inline}x{/jatex}  is a possible value of  {jatex options:inline}X{/jatex}  then  {jatex options:inline}x{/jatex}  - which typically represents the number of successes in  {jatex options:inline}n{/jatex}  trials, must be an integer.
The binomial tables are cumulative, so we only directly look up values of  {jatex options:inline}P(X \le x){/jatex}  for particular values of  {jatex options:inline}n, \: p{/jatex}.
The following rules apply.
{jatex options:inline}P(X \lt x) = P(X \le x-1){/jatex}
{jatex options:inline}P(X \gt x) = 1-P(X \le x){/jatex}
{jatex options:inline}P(X \ge x) = 1-P(X \le x-1){/jatex}
Suppose then that a particular random variable  {jatex options:inline}X{/jatex}  follows a binomial distribution  {jatex options:inline}B(10,0.4){/jatex}
{jatex options:inline}P(X \lt 3) = P(X \le 2)=0.1673{/jatex}
{jatex options:inline}P(X \gt 4) = 1-P(X \le 4)=1-0.6331=0/3669{/jatex}
{jatex options:inline}P(X \ge 2) = 1-P(X \le 1)=1-0.0464=0.9536{/jatex}