Question

A phone survey has a margin error of +/– 4%. What is the range of number of people who will vote for the other candidate if 87 of 114 people said they would vote for the other person and there are 9918 people in the district?

Answer 1

You should divide 87 by 114 for the precent of people. 76% with an margin either way is between 80% and 72%.

Answer 2

7,171 to 7,964 people would vote for the other candidate.

Explanation:

To know the percentage that 87 represents with respect to 114, we have to do the following calculation: 87 / 114 x 100 = 76.3. So, as we can see, 76.3% of the voters said they would vote for the other candidate.

As this survey has a margin error of +/- 4%, this percentage can go from 72.3% to 80.3%. So, given the fact that there are 9,918 people in the district, we have to multiply the total number of inhabitants by 72.3 and 80.3 and then divide the results by 100, in order to know how many inhabitants would vote for the other candidate:

9,918 x 72.3 / 100 = 7,171

9,918 x 80.3 / 100 = 7,964

As we can see, 7,171 to 7,964 people would vote for the other candidate.