The nicotine content of cigarette brand XX (nicotine content/cigarette, mg) can be assumed to follow the 𝑁(𝜇,𝜎2) distribution. A researcher wants to calculate a 99% confidence interval for the unknown parameter 𝜇 and randomly selects eight cigarettes of cigarette brand XX for his study. The nicotine contents of these cigarettes were measured and were:

0.44 0.49 0.43 0.36 0.55 0.59 0.42 0.52

What does parameter 𝜇 describe?

Question 8 Choose one:

a.
The standard deviation of the nicotine content of all cigarettes of cigarette brand XX.

b.
The observed nicotine content of one cigarette of cigarette brand XX.

c.
The average nicotine content of cigarettes of cigarette brand XX in a random sample of eight.

d.
The number of cigarettes in the sample.

e.
The average nicotine content of all cigarettes of cigarette brand XX.

The correct answer is:

**e. The average nicotine content of all cigarettes of cigarette brand XX.**

### Explanation:
The parameter \( \mu \) in a \( N(\mu, \sigma^2) \) distribution represents the population mean of the variable being studied. In this case, \( \mu \) describes the average nicotine content of **all** cigarettes of brand XX, not just the observed sample. 

If you have more questions or would like details on why other options are incorrect, let me know! 

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### Expanding Questions:
1. What is the difference between a population mean (\( \mu \)) and a sample mean (\( \bar{x} \))?
2. Why is it important to assume a normal distribution in this case?
3. How do you calculate a 99% confidence interval for \( \mu \)?
4. What does the parameter \( \sigma^2 \) represent in this context?
5. How would the result change if the sample size were larger?

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### Tip:
When interpreting parameters in a statistical distribution, always identify whether the description refers to the entire population or just a sample. This distinction is crucial in statistics.

The nicotine content of cigarette brand XX (nicotine content/cigarette, mg) can be assumed to follow the 𝑁(𝜇,𝜎2) distribution. A researcher wants to calculate a 99% confidence interval for the unknown parameter 𝜇 and randomly selects eight cigarettes of cigarette brand XX for his study. The nicotine contents of these cigarettes were measured and were: 0.44 0.49 0.43 0.36 0.55 0.59 0.42 0.52. What does parameter 𝜇 describe? Choose one: a. The standard deviation of the nicotine content of all cigarettes of cigarette brand XX. b. The observed nicotine content of one cigarette of cigarette brand XX. c. The average nicotine content of cigarettes of cigarette brand XX in a random sample of eight. d. The number of cigarettes in the sample. e. The average nicotine content of all cigarettes of cigarette brand XX.

Learn how to interpret the parameter μ in a normal distribution when analyzing the nicotine content of cigarette brand XX. This example includes measured data, the difference between population and sample means, and a 99% confidence interval calculation. Perfect for high school or introductory college-level statistics.

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