https://file.aiquickdraw.com/mathbot/file/17303588843061jr05ahw.jpg

To solve this, we’ll calculate the 95% confidence interval for the proportion of voters who were against school bond measures.

### Step-by-Step Solution

1. **Identify Sample Proportion**:
   - Number of voters against school bonds: \( 485 \)
   - Total number of voters sampled: \( 1000 \)
   - Sample proportion \( \hat{p} = \frac{485}{1000} = 0.485 \)

2. **Determine the Z-Score for a 95% Confidence Level**:
   - The Z-score for a 95% confidence level is \( 1.960 \) (as provided in the image).

3. **Calculate the Standard Error**:
   \[
   \text{Standard Error} = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} = \sqrt{\frac{0.485 \times (1 - 0.485)}{1000}}
   \]
   \[
   = \sqrt{\frac{0.485 \times 0.515}{1000}} = \sqrt{\frac{0.249775}{1000}} \approx 0.0158
   \]

4. **Calculate the Margin of Error**:
   \[
   \text{Margin of Error} = Z \times \text{Standard Error} = 1.960 \times 0.0158 \approx 0.030968
   \]

5. **Construct the Confidence Interval**:
   \[
   \text{Lower Bound} = \hat{p} - \text{Margin of Error} = 0.485 - 0.030968 \approx 0.454
   \]
   \[
   \text{Upper Bound} = \hat{p} + \text{Margin of Error} = 0.485 + 0.030968 \approx 0.516
   \]

### Final Answer
The 95% confidence interval is approximately:
\[
0.454 \leq p \leq 0.516
\]

Would you like more details or have any questions?

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Here are 5 related questions to expand your understanding:
1. How would the confidence interval change if the confidence level was 99% instead of 95%?
2. How does the sample size affect the width of the confidence interval?
3. What is the interpretation of a 95% confidence interval?
4. If only 200 people were surveyed, how would that affect the confidence interval for the same proportion?
5. What happens to the confidence interval if the sample proportion is closer to 0 or 1?

**Tip**: Increasing the sample size narrows the confidence interval, providing a more precise estimate of the population proportion.

In a poll of 1000 randomly selected voters in a local election, 485 voters were against school bond measures. Find the 95% confidence interval for the proportion of voters against school bond measures.

Calculate the 95% confidence interval for the proportion of voters against school bond measures from a sample of 1000 voters, with 485 opposing the measures. Understand key statistical concepts such as confidence intervals, standard error, and margin of error. Ideal for high school students in Grades 11-12.

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