Question

In a recent survey, 80% of the community favored building a police substation in their neighborhood. If 15 citizens are chosen, what is the mean number favoring the substation?

Answer 1

Answer:

The mean number favoring the substation is 12 citizens.

Step-by-step explanation:

For each citizen surveyed, there are only two possible outcomes. EIther they favored building a police substation in their neighborhood, or they opposed. This means that we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, with p probability, and X can only have two outcomes.

Has an expected value of:

$E(X) = np$

In this problem, we have that:

$n = 15, p = 0.8$

E(X) = 15*0.8 = 12.

The mean number favoring the substation is 12 citizens.