In a certain town, 22% of voters favor a given ballot measure. For groups of 21 voters, find the variance for the number who favor the measure.
A) $3.6$ voters $^ { 2 }$
B) $4.6$ voters $^ { 2 }$
C) $1.9$ voters $^ { 2 }$
D) 13 voters $^ { 2 }$

Question

In a certain town, 22% of voters favor a given ballot measure. For groups of 21 voters, find the variance for the number who favor the measure. 
A) $3.6$ voters $^ { 2 }$
B) $4.6$ voters $^ { 2 }$
C) $1.9$ voters $^ { 2 }$
D) 13 voters $^ { 2 }$

Quizplus · Accepted Answer

The variance for a binomial distribution is given by the formula $\sigma^2 = np(1-p)$, where $n$ is the number of trials (in this case, voters, which is 21) and $p$ is the probability of success (in this case, the probability that a voter favors the measure, which is 0.22). Plugging in the values, we get $\sigma^2 = 21(0.22)(1-0.22) = 21(0.22)(0.78) = 3.6$ voters$^2$.

In a Certain Town, 22% of Voters Favor a Given 3.63.63.6

In a Certain Town, 22% of Voters Favor a Given $3.6$