Answered

Poll Results
\begin{tabular}{|l|l|}
\hline
Angel Cruz & 483 \\
\hline
Terry Smith & 320 \\
\hline
\end{tabular}

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?

A. 163
B. 1,304
C. 3,864
D. 5,621



Answer :

GinnyAnswer
Sure, let's solve this problem step by step.

1. Determine the total number of votes in the poll:
- Angel Cruz received 483 votes.
- Terry Smith received 320 votes.
- Total votes: [tex]\( 483 + 320 = 803 \)[/tex].

2. Calculate the proportion of votes each candidate received in the poll:
- Proportion of votes for Angel Cruz: [tex]\(\frac{483}{803}\)[/tex].
- Proportion of votes for Terry Smith: [tex]\(\frac{320}{803}\)[/tex].

These proportions are approximately:
- Angel Cruz: [tex]\(0.6015\)[/tex]
- Terry Smith: [tex]\(0.3985\)[/tex]

3. Given that 6,424 people are expected to vote in the actual election, use these proportions to estimate the number of votes each candidate would get:
- Expected votes for Angel Cruz: [tex]\(0.6015 \times 6424 \approx 3864\)[/tex].
- Expected votes for Terry Smith: [tex]\(0.3985 \times 6424 \approx 2560\)[/tex].

4. Calculate the expected number of votes Angel Cruz would win by:
- [tex]\( 3864 - 2560 = 1304 \)[/tex].

So, Angel Cruz is expected to win by 1,304 votes.

The answer is B) 1,304.