Question

A voter polling research group determined that 30% of the voters in a county would vote for the democratic candidate with a ±4% margin of error. If they anticipate only 12,000 people will turn out to vote in this election, which would represent the lowest possible number of voters for the democratic candidate.

Answer 1

Minimum number of voters for the democratic candidate would be 3120 voters.

Explanation:

Total number of people turning out to vote = 12,000

Percentage of votes a democratic would get = 30%

Which means that it is expected that a democratic candidate will get: 30/100 · 12,000 = 3600 votes

However, the polling may have an error of +4% to -4%

Which means that the votes a democratic candidate will get will range from 30%+4% = 34% to 30%-4%= 26% of the total people who turn out to vote

Minimum number of voters can be determined by taking 26% of the total people who turn out to vote:

Minimum number of votes = 26/100 · 12,000 = 3120