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% .
Write the inequality representing the possible percentage of votes: 50% ≤ x ≤ 58% .
The correct inequality 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 possible percentage 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% .
Writing the Inequality The inequality that represents the possible percentage of votes, x , for candidate A is: 50% ≤ x ≤ 58% .
Finding the Correct Option Comparing the inequality with the given options, we find that the correct option is 50 ≤ x ≤ 58 .
Final Answer Therefore, the predicted possible percent of votes, x , for candidate A is represented by the inequality 50 ≤ x ≤ 58 .
Examples
Understanding margins of error is crucial in many real-world applications, such as interpreting survey results, assessing the accuracy of scientific measurements, and evaluating the reliability of statistical models. For instance, if a medical study reports that a new drug is effective with a margin of error, knowing the range of possible effectiveness helps doctors make informed decisions about patient care. Similarly, in market research, understanding the margin of error in customer satisfaction surveys allows companies to gauge the true level of customer happiness and identify areas for improvement. These concepts are also vital in financial analysis, where understanding the range of possible outcomes helps investors manage risk and make sound investment decisions.
The inequality representing the predicted possible percent of votes for candidate A is 50 ≤ x ≤ 58 . This is calculated by accounting for a margin of error of 4% above and below the predicted 54% . Therefore, the correct answer is option A.
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