Suppose x has a normal dstribution with s- 1.9. A random sample of sizn 70 has a sample mean of x- 20. (a) What conditions are necessary for your cakculations? (Seiect all that apply.) 1 is unknown is known uniform distribution of x normal distribution of x (b) Find a 9% contidence interval for mu. What is the margin of error? (Raund your anawers to two decimal places, lower limit upper limt margin of error

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**Transcription for Educational Website**

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**Problem Statement:**

Suppose \( x \) has a normal distribution with \( \sigma = 1.9 \). A random sample of size 70 has a sample mean of \( \bar{x} = 20 \).

**Question (a): What conditions are necessary for your calculations? (Select all that apply.)**

- [ ] \( \sigma \) is unknown
- [x] \( \sigma \) is known
- [ ] Uniform distribution of \( x \)
- [x] Normal distribution of \( x \)

**Explanation:**  
The conditions necessary for the calculations are that the standard deviation \( \sigma \) is known and that the distribution of \( x \) is normal. These are checked in the options provided.

**Question (b): Find a 95% confidence interval for \( \mu \). What is the margin of error? (Round your answers to two decimal places.)**

- **Lower limit:** [            ]
- **Upper limit:** [            ]
- **Margin of error:** [            ]

**Note:**  
Values and calculations for the confidence interval lower limit, upper limit, and margin of error require input and computation based on the sample statistics provided.

---

This problem requires understanding of normal distributions, confidence intervals, and the conditions for inference in statistics.
Transcribed Image Text:**Transcription for Educational Website** --- **Problem Statement:** Suppose \( x \) has a normal distribution with \( \sigma = 1.9 \). A random sample of size 70 has a sample mean of \( \bar{x} = 20 \). **Question (a): What conditions are necessary for your calculations? (Select all that apply.)** - [ ] \( \sigma \) is unknown - [x] \( \sigma \) is known - [ ] Uniform distribution of \( x \) - [x] Normal distribution of \( x \) **Explanation:** The conditions necessary for the calculations are that the standard deviation \( \sigma \) is known and that the distribution of \( x \) is normal. These are checked in the options provided. **Question (b): Find a 95% confidence interval for \( \mu \). What is the margin of error? (Round your answers to two decimal places.)** - **Lower limit:** [ ] - **Upper limit:** [ ] - **Margin of error:** [ ] **Note:** Values and calculations for the confidence interval lower limit, upper limit, and margin of error require input and computation based on the sample statistics provided. --- This problem requires understanding of normal distributions, confidence intervals, and the conditions for inference in statistics.
Suppose \( x \) has a normal distribution with \( \sigma = 1.1 \). A random sample of size 10 has a sample mean of \( \bar{x} = 50 \).

(a) What conditions are necessary for your calculations? (Select all that apply.)

- [x] \( \sigma \) is known
- [x] normal distribution of \( x \)
- [ ] uniform distribution of \( x \)
- [ ] \( \sigma \) is unknown

(b) Find a 90% confidence interval for \( \mu \). What is the margin of error? (Round your answers to two decimal places.)

- Lower limit: [ ]
- Upper limit: [ ]
- Margin of error: [ ]
Transcribed Image Text:Suppose \( x \) has a normal distribution with \( \sigma = 1.1 \). A random sample of size 10 has a sample mean of \( \bar{x} = 50 \). (a) What conditions are necessary for your calculations? (Select all that apply.) - [x] \( \sigma \) is known - [x] normal distribution of \( x \) - [ ] uniform distribution of \( x \) - [ ] \( \sigma \) is unknown (b) Find a 90% confidence interval for \( \mu \). What is the margin of error? (Round your answers to two decimal places.) - Lower limit: [ ] - Upper limit: [ ] - Margin of error: [ ]
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