A political polling agency predicts candidate A will win an election with $54 \%$ of the votes. Their poll has a margin of error of $4 \%$ both above and below the predicted percentage. Which inequality represents the predicted possible percent of votes, $x$, for candidate $A$?
A. $50 \leq x \leq 58$
B. $x \geq 50$ or $x \leq 58$
C. $x \geq 52$ or $x \leq 56$
D. $52 \leq x \leq 56$
Answer (2)
Calculate the upper bound by adding the margin of error to the predicted percentage: 54% + 4% = 58% .
Calculate the lower bound by subtracting the margin of error from the predicted percentage: 54% − 4% = 50% .
Express the possible percentage of votes, x , as an inequality between the lower and upper bounds: 50 ≤ x ≤ 58 .
The inequality representing the predicted possible percent of votes for candidate A is 50 ≤ x ≤ 58 .
Explanation
Understanding the Problem The problem states that a political polling agency predicts candidate A will win an election with 54% of the votes. The poll has a margin of error of 4% both above and below the predicted percentage. We need to find the inequality that represents the predicted possible percent of votes, x , for candidate A .
Calculating the Upper Bound To find the upper bound of the possible percentage of votes, we add the margin of error to the predicted percentage: 54% + 4% = 58% .
Calculating the Lower Bound To find the lower bound of the possible percentage of votes, we subtract the margin of error from the predicted percentage: 54% − 4% = 50% .
Expressing the Inequality The possible percentage of votes, x , can be expressed as an inequality between the lower and upper bounds: 50 ≤ x ≤ 58 .
Final Answer Therefore, the inequality that represents the predicted possible percent of votes, x , for candidate A is 50 ≤ x ≤ 58 .
Examples
In real-world scenarios, understanding margins of error is crucial in various fields, such as political polling, scientific research, and market analysis. For instance, if a survey predicts a product will receive 60% of the market share with a margin of error of 5% , the actual market share could range from 55% to 65% . This range helps businesses make informed decisions about production, marketing, and investment strategies, accounting for the uncertainty inherent in predictions.
The predicted possible percentage of votes, x , for candidate A is represented by the inequality 50 ≤ x ≤ 58 . This indicates that candidate A could receive between 50% and 58% of the votes based on the margin of error. Thus, the correct answer is option A.
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