Here are the confidence intervals with their corresponding confidence levels:

1. $\bar{x} \pm 1.282\left(\frac{\sigma}{\sqrt{n}}\right)$ corresponds to A. 80% confidence level.
2. $\bar{x} \pm 1.96\left(\frac{\sigma}{\sqrt{n}}\right)$ corresponds to B. 95% confidence level.
3. $\bar{x} \pm 2.575\left(\frac{\sigma}{\sqrt{n}}\right)$ corresponds to C. 99% confidence level.

Explanation:

• The z-score of 1.282 is associated with an 80% confidence level.
• The z-score of 1.96 is commonly used for a 95% confidence level.
• The z-score of 2.575 is used for a 99% confidence level.

Would you like a detailed explanation of how these z-scores are derived from the standard normal distribution?

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Here are 5 related questions to explore further:

1. What is the relationship between confidence level and margin of error?
2. How is the confidence interval for a sample proportion calculated?
3. What is the effect of increasing the sample size on the confidence interval?
4. How do you calculate the required sample size for a desired confidence level and margin of error?
5. How do you interpret a 95% confidence interval in practical terms?

Tip: Increasing the confidence level widens the confidence interval, while decreasing it makes the interval narrower.