A population of values has a normal distribution with  and . You intend to draw a random sample of size .

What is the mean of the distribution of sample means?
 
 

What is the standard deviation of the distribution of sample means?
(Report answer accurate to 2 decimal places.)
 
 


To answer your question about the distribution of sample means, we'll use the properties of the normal distribution.

1. **Mean of the Distribution of Sample Means**: The mean of the distribution of sample means (also known as the sampling distribution) is equal to the mean of the population. If the population mean is denoted as \(\mu\), then the mean of the sample means is also \(\mu\).

2. **Standard Deviation of the Distribution of Sample Means**: The standard deviation of the distribution of sample means, also known as the standard error (SE), is calculated using the formula:
   \[
   \text{SE} = \frac{\sigma}{\sqrt{n}}
   \]
   where \(\sigma\) is the standard deviation of the population and \(n\) is the sample size.

To provide specific numerical answers, please supply the population mean (\(\mu\)), the population standard deviation (\(\sigma\)), and the sample size (\(n\)).

A population of values has a normal distribution with μ and σ. You intend to draw a random sample of size n. What is the mean of the distribution of sample means? What is the standard deviation of the distribution of sample means?

Calculate the mean and standard deviation of the sampling distribution for a normally distributed population with given parameters. This problem explores key concepts in statistics, including the Central Limit Theorem and the formula for standard error. Ideal for students in Grades 11-12.

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