## Using Binomial Distribution Tables

Th binomial distribution is discrete. This means that if a random variable
$X$
follows a binomial distribution
$B(n,p)$
and
$x$
is a possible value of
$X$
then
$x$
- which typically represents the number of successes in
$n$
trials, must be an integer.
The binomial tables are cumulative, so we only directly look up values of
$P(X \le x)$
for particular values of
$n, \: p$
.
The following rules apply.
$P(X \lt x) = P(X \le x-1)$

$P(X \gt x) = 1-P(X \le x)$

$P(X \ge x) = 1-P(X \le x-1)$

Suppose then that a particular random variable
$X$
follows a binomial distribution
$B(10,0.4)$

$P(X \lt 3) = P(X \le 2)=0.1673$

$P(X \gt 4) = 1-P(X \le 4)=1-0.6331=0/3669$

$P(X \ge 2) = 1-P(X \le 1)=1-0.0464=0.9536$