In a recent survey, 64% of the community favored building a police substation in their neighborhood. If 14 citizens are chosen, find the probability that exactly 8 of them favor the building of the police substation.
A)0.184
B)0.058
C)0.571
D)0.640

Question

Quizplus · Accepted Answer

This is a binomial probability problem where n = 14 (number of trials), k = 8 (number of successes), and p = 0.64 (probability of success). The formula for binomial probability is P(X = k) = (nCk) * p^k * (1-p)^(n-k). Plugging in the values: P(X = 8) = (14C8) * (0.64)^8 * (0.36)^6 ≈ 0.184.

In a Recent Survey, 64% of the Community Favored Building