Answer:
Probability that exactly 5 of them favor the building of the health center is 0.0408.
Step-by-step explanation:
We are given that in a recent survey, 60% of the community favored building a health center in their neighborhood. 
Also, 14 citizens are chosen.
The above situation can be represented through Binomial distribution;

where, n = number of trials (samples) taken = 14 citizens
          r = number of success = exactly 5
         p = probability of success which in our question is % of the community
               favored building a health center in their neighborhood, i.e; 60%
<em>LET X = Number of citizens who favored building of the health center.</em>
So, it means X ~ 
Now, Probability that exactly 5 of them favor the building of the health center is given by = P(X = 5)
         P(X = 5) = 
                       = 
                       = 0.0408
Therefore, Probability that exactly 5 of them favor the building of the health center is 0.0408.