Question

In a recent survey, 66% of the community favored building a health center in their neighborhood. Suppose 12 citizens are randomly chosen and asked if they favor building the health center. Assume all requirements for computing a binomial probability are met. What is the probability that exactly 10 of the 12 individuals favor building the health center? (Round your answer to 4 decimal places)

Answer 1

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.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

66% of the community favored building a health center in their neighborhood.

This means that $p = 0.66$

12 citizens

This means that $n = 12$

What is the probability that exactly 10 of the 12 individuals favor building the health center?

This is P(X = 10).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{12,10}.(0.66)^{10}.(0.34)^{2} = 0.1197$

0.1197 = 11.97% probability that exactly 10 of the 12 individuals favor building the health center