A recent survey of 250 citizens showed that 56% favored a renovation project for the local library. The survey had a margin of error of ±1.9%. If the town has 78,717 registered voters, what is the expected maximum number of voters who would support the project? Round the answer to the nearest whole number.
Question
A recent survey of 250 citizens showed that 56% favored a renovation project for the local library. The survey had a margin of error of ±1.9%. If the town has 78,717 registered voters, what is the expected maximum number of voters who would support the project? Round the answer to the nearest whole number.
Solution
To find the expected maximum number of voters who would support the project, we need to add the margin of error to the percentage of citizens who favored the project and then apply that percentage to the total number of registered voters.
Here are the steps:
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Add the margin of error to the percentage of citizens who favored the project: 56% + 1.9% = 57.9%.
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Convert the percentage to a decimal by dividing by 100: 57.9 / 100 = 0.579.
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Multiply the total number of registered voters by the decimal: 78,717 * 0.579 = 45,601.263.
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Round the result to the nearest whole number: 45,601.
So, the expected maximum number of voters who would support the project is 45,601.
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