Question

Find the mean, variance and standard deviation of the binomial experiment. In a recent survey, 70% of the community favored building a police substation in their neighborhood. If 30 citizens are chosen, what is the mean number favoring the substation? What would be the variance and standard deviation of their responses?

Answer 1

Answer: Mean = 21 , Variance = 6.3 , standard deviation =2.51

Explanation:

Formula for the mean, variance and standard deviation of the binomial experiment :

`Mean = np\\\\ Variance = np(1-p)\\\\ Standard\ deviation = √(variance)`

, where n= sample size , p= population proportion.

As per given, p= 70%=0.7 , n=30

`Mean = 0.7*30=21\\\\Variance =(30)(0.7)(1-0.7)=(21)(0.30)=6.3\\\\ Standard\ deviation = √(6.3)\approx2.51`

Hence, Mean = 21 , Variance = 6.3 , standard deviation =2.51