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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?

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JeanaShupp

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

Step-by-step explanation:

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

[tex]Mean = np\\\\ Variance = np(1-p)\\\\ Standard\ deviation = \sqrt{variance}[/tex]

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

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

[tex]Mean = 0.7\times30=21\\\\Variance =(30)(0.7)(1-0.7)=(21)(0.30)=6.3\\\\ Standard\ deviation = \sqrt{6.3}\approx2.51[/tex]

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

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