A survey has a margin of error of 4%. In the survey, 67 of the 110 people interviewed said they would vote for candidate A. If there are 9570 people in the district, what is the range of the number of people who will vote for candidate A?

Question

Mathematics

Hailie Lynch

1 July, 18:14

A survey has a margin of error of 4%. In the survey, 67 of the 110 people interviewed said they would vote for candidate A. If there are 9570 people in the district, what is the range of the number of people who will vote for candidate A?

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Gucci · Answer 1

In this problem, we use ratio and proportion as a solution. In this type of technique, the concept used is that there is a fixed ratio of the voters for candidate A to the total number of voters. Thus, we equate these ratio.

67/100 = x/9570

x denotes the number of voters for candidate A when the actual number of total voters are 9,570. Solving for x, we find that x = 6,411.9. In approximation, that is equal to 6,412 voters.

However, you should take not of the margin of error. It means that the number of voters is not exactly 6,412. There is a room for the range which is 4%.

6,412 (0.04) = 256

So, the number of voters is 6,412+/-256.

6,412 + 256 = 6,668

6,412 - 256 = 6,156

Thus, the range of voters is between 6,668 to 6,156 people.