Let Y be the random variable denoting the number of patients that recover from the stomach disease. Y is clearly a binomial random variable as each patient will either recover or not recover (i.e. has only 2 values).

Here, \(n = 20\) and \(p = 0.8\)

We need to find \(P(Y = 14).\) This can be found by using Table I in Appendix 3 with \(n =20\) and \(p = 0.8\)

\(P(Y = 14) = P(Y \leq 14) - P(Y \leq 13)\)

\(= 0.196 - 0.087\)

\(= 0.109\)

Result: \(P(Y = 14) = 0.109\)