In a recent survey, 72% of the community favored building a health center in their neighborhood. If 14 citizensare chosen, find the probability that exactly 10 of them favor the building of the health center.
A) 0.230
B) 0.001
C) 0.714
D) 0.720

Question

Quizplus · Accepted Answer

This is a binomial probability problem where n = 14 (number of trials), k = 10 (number of successes), and p = 0.72 (probability of success on a single trial). The binomial probability formula is P(X = k) = (n choose k) * p^k * (1-p)^(n-k). Plugging in the values: P(X = 10) = (14 choose 10) * (0.72)^10 * (0.28)^4 ≈ 0.230.

In a Recent Survey, 72% of the Community Favored Building