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. 1.9
b. 13
c. 4.6
d. 3.6

Answer 1

The variance for the number of voters who favor the ballot measure in groups of 21 is calculated using the formula for a binomial distribution, which yields an answer of 3.78. The closest option to this value is 3.6, answer option d.

Step-by-step explanation:

In the question about a town where 22% of voters favor a given ballot measure, we are asked to find the variance for the number of voters who favor the measure in groups of 21 voters. To calculate the variance, we use the formula for the variance of a binomial distribution, which is np(1-p), where 'n' is the number of trials (voters in this case), 'p' is the probability of a voter favoring the measure, and '1-p' is the probability of a voter not favoring the measure.

Using the information provided:

• n = 21 (the number of voters in a group)
• p = 0.22 (the probability of a voter favoring the measure)

Thus, the variance (Var) is:

Var = np(1-p) = 21 × 0.22 × (1 - 0.22) = 21 × 0.22 × 0.78 = 3.78

The closest answer to 3.78 is 3.6, which is option d.