Question

A political polling agency predicts candidate A will win an election with 63% of the votes. Their poll has a margin of error of 7% both above and below the predicted percentage. Which inequality represents the predicted possible percent of votes, x, for candidate A?

Answer 1

56% ≤ p ≤ 70%

Explanation:

Given the following :

Predicted % of votes to win for candidate A= 63%

Margin of Error in prediction = ±7%

Which inequality represents the predicted possible percent of votes, x, for candidate A?

Let the interval = p

Hence,

|p - prediction| = margin of error

|p - 63%| = ±7%

Hence,

Upper boundary : p = +7% + 63% = 70%

Lower boundary : p = - 7% + 63% = 56%

Hence,

Lower boundary ≤ p ≤ upper boundary

56% ≤ p ≤ 70%