\[X\]
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 \[B(10,0.4)\]
\[P(X \lt 3) = P(X \le 2)=0.1673\]
\[P(X \gt 4) = 1-P(X \le 4)=1-0.6331=0/3669\]
\[P(X \ge 2) = 1-P(X \le 1)=1-0.0464=0.9536\]