In a recent survey 61 of the community favored building a p

In a recent survey, 61 % of the community favored building a police substation in their neighborhood. If 14 citizens are chosen , find the probability that exactly 6 out of them favor the building of the police substation

Solution

Given p=61/100=0.61, q=1-p=1-0.61=0.39, n=14.

By using binomial distribution, P(X=6)=(14c6)*((0.61)⁶)*((0.39)⁸)=(3003)*(0.0515)*(0.000535)=0.0827.