A random sample with size n = 9 is drawn from a population that follows normal distribution with mean of 10 and standard deviation of 6. What is the mean of all sample means of size 9?

In statistics, the mean of all sample means (also known as the expected value of the sample means) is equal to the population mean. 

Given that the population has a mean (μ) of 10, the mean of all sample means for a sample size of \( n = 9 \) is also:

\[
\text{Mean of sample means} = \mu = 10
\]

If you have any questions or need further clarification, feel free to ask! Here are some related questions you might consider:

1. How does the Central Limit Theorem apply to this scenario?
2. What is the standard error of the sample means for this sample size?
3. How does the sample size affect the distribution of sample means?
4. What would happen if the sample size were larger or smaller?
5. How can we use this information to estimate population parameters?

**Tip:** Understanding the properties of the sampling distribution can help in making inferences about the population from sample data.

Learn how to calculate the mean of all sample means for a normally distributed population with a given mean of 10 and standard deviation of 6. This problem uses key statistical concepts, such as the expected value of sample means and the Central Limit Theorem, suitable for introductory college-level statistics.

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