Answer:
[tex]P(X \geq 13) = 0.021[/tex]
Step-by-step explanation:
From the question we are told that:
Probability of curing patients P(x)=0.65
Sample size n=14
Generally the Binomial equation is mathematically given by
[tex]P(X) =\frac{(n!)}{X!(n-X)!))} *p^X*(1-p)^(n-X)[/tex]
Generally the equation for Equation for at least 12 cured is mathematically given by
[tex]P(X \geq 13) = P(X = 13)+P(X = 14)[/tex]
For [tex]P(X = 13)[/tex]
[tex]P(X = 13) = (14!/(13!(14-13)!))*0.65^13*(1-0.65)^(14-13) \\\\P(X = 13)= 0.018116[/tex]
For [tex]P(X = 14)[/tex]
[tex]P(X = 14) = (14!/(14!(14-14)!))*0.65^14*(1-0.65)^(14-14) \\\\P(X = 14)= 0.00240318[/tex]
Therefore
[tex]P(X \geq 13) =P(X = 13)+P(X = 14)[/tex]
[tex]P(X \geq 13) = 0.018116+0.00240318[/tex]
[tex]P(X \geq 13) = 0.02051918[/tex]
[tex]P(X \geq 13) = 0.021[/tex]
