**Text Transcription for Educational Website:** --- From a random sample of 24 months from January 2006 through December 2016, the mean number of tornadoes per month in the United States was about 100. Assume the population standard deviation is 114. Construct a 90% confidence interval for the population mean. --- **Explanation:** The problem involves constructing a 90% confidence interval for the population mean based on the given sample data. Here's a breakdown of the steps needed to solve this: 1. **Sample Mean (x̄):** 100 tornadoes per month 2. **Population Standard Deviation (σ):** 114 3. **Sample Size (n):** 24 To construct the confidence interval, the following formula is used: \[ \text{Confidence Interval} = x̄ \pm Z \left( \frac{\sigma}{\sqrt{n}} \right) \] Where: - \( x̄ \) is the sample mean. - \( Z \) is the Z-score corresponding to the 90% confidence level (approximately 1.645). - \( \sigma \) is the population standard deviation. - \( n \) is the sample size. By plugging in the values, you can calculate the margin of error and then determine the confidence interval.
**Text Transcription for Educational Website:** --- From a random sample of 24 months from January 2006 through December 2016, the mean number of tornadoes per month in the United States was about 100. Assume the population standard deviation is 114. Construct a 90% confidence interval for the population mean. --- **Explanation:** The problem involves constructing a 90% confidence interval for the population mean based on the given sample data. Here's a breakdown of the steps needed to solve this: 1. **Sample Mean (x̄):** 100 tornadoes per month 2. **Population Standard Deviation (σ):** 114 3. **Sample Size (n):** 24 To construct the confidence interval, the following formula is used: \[ \text{Confidence Interval} = x̄ \pm Z \left( \frac{\sigma}{\sqrt{n}} \right) \] Where: - \( x̄ \) is the sample mean. - \( Z \) is the Z-score corresponding to the 90% confidence level (approximately 1.645). - \( \sigma \) is the population standard deviation. - \( n \) is the sample size. By plugging in the values, you can calculate the margin of error and then determine the confidence interval.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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![**Text Transcription for Educational Website:**
---
From a random sample of 24 months from January 2006 through December 2016, the mean number of tornadoes per month in the United States was about 100. Assume the population standard deviation is 114.
Construct a 90% confidence interval for the population mean.
---
**Explanation:**
The problem involves constructing a 90% confidence interval for the population mean based on the given sample data. Here's a breakdown of the steps needed to solve this:
1. **Sample Mean (x̄):** 100 tornadoes per month
2. **Population Standard Deviation (σ):** 114
3. **Sample Size (n):** 24
To construct the confidence interval, the following formula is used:
\[ \text{Confidence Interval} = x̄ \pm Z \left( \frac{\sigma}{\sqrt{n}} \right) \]
Where:
- \( x̄ \) is the sample mean.
- \( Z \) is the Z-score corresponding to the 90% confidence level (approximately 1.645).
- \( \sigma \) is the population standard deviation.
- \( n \) is the sample size.
By plugging in the values, you can calculate the margin of error and then determine the confidence interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36355303-957c-411e-8cde-40ccc370c613%2Fae102a59-c471-4231-bd82-e98caa89ffc9%2Fg9msv6l.jpeg&w=3840&q=75)
Transcribed Image Text:**Text Transcription for Educational Website:**
---
From a random sample of 24 months from January 2006 through December 2016, the mean number of tornadoes per month in the United States was about 100. Assume the population standard deviation is 114.
Construct a 90% confidence interval for the population mean.
---
**Explanation:**
The problem involves constructing a 90% confidence interval for the population mean based on the given sample data. Here's a breakdown of the steps needed to solve this:
1. **Sample Mean (x̄):** 100 tornadoes per month
2. **Population Standard Deviation (σ):** 114
3. **Sample Size (n):** 24
To construct the confidence interval, the following formula is used:
\[ \text{Confidence Interval} = x̄ \pm Z \left( \frac{\sigma}{\sqrt{n}} \right) \]
Where:
- \( x̄ \) is the sample mean.
- \( Z \) is the Z-score corresponding to the 90% confidence level (approximately 1.645).
- \( \sigma \) is the population standard deviation.
- \( n \) is the sample size.
By plugging in the values, you can calculate the margin of error and then determine the confidence interval.
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