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) $3.6 \text { voters } { } ^ { 2 }$
B) $4.6 \text { voters } { } ^ { 2 }$
C) $1.9 \text { voters } ^ { 2 }$
D) $13 \text { voters } ^ { 2 }$

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) $3.6 \text { voters } { } ^ { 2 }$
B) $4.6 \text { voters } { } ^ { 2 }$
C) $1.9 \text { voters } ^ { 2 }$
D) $13 \text { voters } ^ { 2 }$

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 $\sigma^2 = 21 \times 0.22 \times (1-0.22) = 21 \times 0.22 \times 0.78 = 3.6 \text{ voters}^2$.

In a Certain Town, 22 % of Voters 3.6 voters 23.6 \text { voters } { } ^ { 2 }3.6 voters 2

In a Certain Town, 22 % of Voters $3.6 \text { voters } { } ^ { 2 }$