Question

In a recent survey, 73% 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

Answer 1

So, the probability is P=0.094.

Explanation:

We know that in a recent survey, 73% of the community favored building a police substation in their neighborhood.

We get that p=0.73 and q=1-0.73=0.27.

We calculate the probability that exactly 8 of them favor the building of the police substation, if 14 citizens are chosen.

We get that n=14 and k=8.

We calculate the probability:

`P=C_k^n\cdot p^k\cdot q^(n-k)\\\\P=C_8^(14)\cdot 0.73^8\cdot 0.27^6\\\\P=3003\cdot 0.00003124\\\\P=0.094\\`

So, the probability is P=0.094.