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Problem-Solving and Data Analysis / Inference from sample statistics and margin of error Difficulty: Hard

Poll Results
Angel Cruz	$483$ $483$
Terry Smith	$320$ $320$

The table shows the results of a poll. A total of $803$ voters selected at random were asked which candidate they would vote for in the upcoming election. According to the poll, if $6,424$ people vote in the election, by how many votes would Angel Cruz be expected to win?

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Explanation

Choice B is correct. It's given that $483$ out of $803$ voters responded that they would vote for Angel Cruz. Therefore, the proportion of voters from the poll who responded they would vote for Angel Cruz is $StartFraction 483 Over 803 EndFraction$ . It’s also given that there are a total of $6,424$ voters in the election. Therefore, the total number of people who would be expected to vote for Angel Cruz is $6,424 left parenthesis StartFraction 483 Over 803 EndFraction right parenthesis$ , or $3,864$ . Since $3,864$ of the $6,424$ total voters would be expected to vote for Angel Cruz, it follows that $6,424 minus 3,864$ , or $2,560$ voters would be expected not to vote for Angel Cruz. The difference in the number of votes for and against Angel Cruz is $3,864 minus 2,560$ , or $1,304$ votes. Therefore, if $6,424$ people vote in the election, Angel Cruz would be expected to win by $1,304$ votes.

Choice A is incorrect. This is the difference in the number of voters from the poll who responded that they would vote for and against Angel Cruz.

Choice C is incorrect. This is the total number of people who would be expected to vote for Angel Cruz.

Choice D is incorrect. This is the difference between the total number of people who vote in the election and the number of voters from the poll.