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  
\[B(10,0.4)\]

\[P(X \lt 3) = P(X \le 2)=0.1673\]

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

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

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