Question
Before a school election, a sample of voters gave Karim 28 votes, Marisol 41, and Richard 11. Based on these results, predict the number of votes for each candidate if 1600 students vote.
Answers
GPT-4o mini
To predict the number of votes for each candidate based on the given sample, we first need to calculate the total number of votes in the sample and then determine the proportion of votes each candidate received.
The total number of votes in the sample is:
\[ 28 + 41 + 11 = 80. \]
Next, we find the proportion of votes for each candidate:
- For Karim:
\[ \text{Proportion}_{\text{Karim}} = \frac{28}{80} = 0.35. \]
- For Marisol:
\[ \text{Proportion}_{\text{Marisol}} = \frac{41}{80} = 0.5125. \]
- For Richard:
\[ \text{Proportion}_{\text{Richard}} = \frac{11}{80} = 0.1375. \]
Now, we can predict the number of votes for each candidate based on a total of 1600 votes:
- Predicted votes for Karim:
\[ 0.35 \times 1600 = 560. \]
- Predicted votes for Marisol:
\[ 0.5125 \times 1600 = 820. \]
- Predicted votes for Richard:
\[ 0.1375 \times 1600 = 220. \]
Therefore, the predicted number of votes for each candidate is:
- Karim: **560 votes**
- Marisol: **820 votes**
- Richard: **220 votes**
The total number of votes in the sample is:
\[ 28 + 41 + 11 = 80. \]
Next, we find the proportion of votes for each candidate:
- For Karim:
\[ \text{Proportion}_{\text{Karim}} = \frac{28}{80} = 0.35. \]
- For Marisol:
\[ \text{Proportion}_{\text{Marisol}} = \frac{41}{80} = 0.5125. \]
- For Richard:
\[ \text{Proportion}_{\text{Richard}} = \frac{11}{80} = 0.1375. \]
Now, we can predict the number of votes for each candidate based on a total of 1600 votes:
- Predicted votes for Karim:
\[ 0.35 \times 1600 = 560. \]
- Predicted votes for Marisol:
\[ 0.5125 \times 1600 = 820. \]
- Predicted votes for Richard:
\[ 0.1375 \times 1600 = 220. \]
Therefore, the predicted number of votes for each candidate is:
- Karim: **560 votes**
- Marisol: **820 votes**
- Richard: **220 votes**