Respuesta :
Answer:
0.085
Explanation:
To find the probability, we will use the binomial distribution because there are n identical events ( 14 citizens), with a probability of success (p = 60%). Then, the probability can be calculated as:
[tex]P(x)=\text{nCx}\cdot p^x\cdot(1-p)^{n-x}[/tex]Where nCx is equal to
[tex]\text{nCx}=\frac{n!}{x!(n-x)!}[/tex]So, to find the probability that exactly 11 of them favor the building of the health center, we need to replace x = 11, n = 14, and p = 0.6
[tex]14C11=\frac{14!}{11!(14-11)!}=\frac{14!}{11!(3!)}=364[/tex][tex]\begin{gathered} P(11)=364(0.6)^{11}(1-0.6)^{14-11} \\ P(11)=0.085 \end{gathered}[/tex]Therefore, the probability that exactly 11 of them favor the building of the health center is 0.085
