Question

18. In a recent survey, 75% of the community favored building a police substation in their neighborhood. If 10 citizens are chosen, find the probability that exactly 8 of them favor the building of the police substation.

Answer 1

Answer: 0.28157

Explanation:

Given, The proportion of the community favored building a police substation in their neighborhood: p= 0.75

Number of citizens are chosen: n= 10

Let x be the binomial variable that represents the number of citizens favor the building of the police substation.

Then, the probability that exactly 8 of them favor the building of the police substation will be :

`P(x=8)=\ ^(10)C_8(0.75)^8(1-0.75)^2`

[Using binomial probability function
`P(X=x)=^nC_xp^x(1-p)^(n-x)`]

`=(10!)/(8!2!)(0.100113)(0.0625)\\\\=0.2815678125\approx0.28157`

Hence, the probability that exactly 8 of them favor the building of the police substation =0.28157