Question

The results of a poll indicate that between 33% and 37% of the population of a town visit the library at least once a year.

What is the poll’s margin of error?



Enter your answer in the box.

±___%

Answer 1

The interval given was 33% to 37%

This means that subtracting the margin of error from the percentage of the population that visit the library once a year gives the lower end and adding the margin of error to the percentage of the population that visit the library once a year gives the upper end

Let x denote margin of error and y denotes the percentages of the population that visit the library once a year

we can get the following equations and solve for the values of x and y


`y - x = 33\%.......eqn1 \\ y + x = 37\%........eqn2`

Adding eqn1 and eqn2 to gives



`2y = 70\% \\ y = 35\%`

Putting the value of y into any of the equations



`35\% + x = 37\% \\ x = 37\% - 35\% \\ x = 2\%`

Thus, the margin of error is

`\pm2\%`


Therefore we enter 2 in the box