Respuesta :
Answer:
0.1197 = 11.97% probability that exactly 10 of the 12 individuals favor building the health center
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
66% of the community favored building a health center in their neighborhood.
This means that [tex]p = 0.66[/tex]
12 citizens
This means that [tex]n = 12[/tex]
What is the probability that exactly 10 of the 12 individuals favor building the health center?
This is P(X = 10).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{12,10}.(0.66)^{10}.(0.34)^{2} = 0.1197[/tex]
0.1197 = 11.97% probability that exactly 10 of the 12 individuals favor building the health center
