Question

question 17 (4 points)
a survey of a random sample of voters predicts that candidate a will receive 41% of the votes, candidate b will receive 40% of the votes, and candidate c will receive 9% of the votes. the margin of error is ±5%. which statement is correct about the percent of votes that the candidates might get?
a a clear winner can be predicted based on these results.
candidate c will definitely get the highest percentage.
candidate b will not get the highest percentage of votes.
candidate a will get between 36% and 46% of votes.

Explanation:

Step1: Calculate the range for Candidate A

The percentage for Candidate A is \(41\%\) with a margin of error of \(\pm5\%\).
The lower bound is \(41\% - 5\%=36\%\) and the upper bound is \(41\%+ 5\% = 46\%\). So Candidate A's votes are between \(36\%\) and \(46\%\).

Step2: Calculate the range for Candidate B

The percentage for Candidate B is \(40\%\) with a margin of error of \(\pm5\%\).
The lower bound is \(40\% - 5\% = 35\%\) and the upper bound is \(40\%+5\%=45\%\).

Step3: Analyze each option

• Option 1: Candidate A's range is \(36\%-46\%\), so this statement is correct.
• Option 2: Candidate B's upper - bound is \(45\%\) which could be higher than others (if Candidate A's lower - bound is considered), so we can't say Candidate B will not get the highest.
• Option 3: We can't be sure Candidate C will definitely get the highest as there is overlap in ranges.
• Option 4: There is overlap in ranges (e.g., Candidate A's upper - bound and Candidate B's upper - bound), so a clear winner can't be predicted.

Answer:

Candidate A will get between 36% and 46% of votes.