What is the confidence level for the interval x±1.645 ? Vn

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Question:**

What is the confidence level for the interval \(\bar{x} \pm 1.645 \cdot \frac{\sigma}{\sqrt{n}}\)?

**Explanation:**

This expression represents a confidence interval for a population mean \(\bar{x}\), where:
- \(\sigma\) is the population standard deviation.
- \(n\) is the sample size.
- The multiplier 1.645 is the critical value.

The confidence level that corresponds to the critical value of 1.645 is approximately 90%. This is used when the population standard deviation is known and the sample size is large enough to assume a normal distribution of the sample mean by the Central Limit Theorem.
Transcribed Image Text:**Question:** What is the confidence level for the interval \(\bar{x} \pm 1.645 \cdot \frac{\sigma}{\sqrt{n}}\)? **Explanation:** This expression represents a confidence interval for a population mean \(\bar{x}\), where: - \(\sigma\) is the population standard deviation. - \(n\) is the sample size. - The multiplier 1.645 is the critical value. The confidence level that corresponds to the critical value of 1.645 is approximately 90%. This is used when the population standard deviation is known and the sample size is large enough to assume a normal distribution of the sample mean by the Central Limit Theorem.
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