The "Central Limit Theorem will tell us a few important things:

1) The mean of ALL sampling distributions equals the mean of the populaiton. 

2) The standard deviation for a sampling distribution is equal to  where  is the population standard deviation. 

3) For n 30 or larger the sampling distribution should be approximately normal. 

 

If Population mean  = 24.4

Population standard deviation  = 6.49

sample size n = 37

 

The MEAN of the sampling distribution = ________


Based on the Central Limit Theorem, the mean of the sampling distribution is equal to the mean of the population. 

Given the information:
- Population mean (\(\mu\)) = 24.4
- Sample size (\(n\)) = 37

The mean of the sampling distribution is:
\[
\text{Mean of the sampling distribution} = \mu = 24.4
\]

### Answer:
The mean of the sampling distribution = **24.4**

Would you like to go into more details or have any questions?

Here are five related questions to expand your understanding:

1. What is the formula for the standard error of the mean in a sampling distribution?
2. How does increasing the sample size \(n\) affect the standard error of the mean?
3. What happens to the shape of the sampling distribution if the sample size is less than 30?
4. Why does the Central Limit Theorem assume that the sampling distribution becomes approximately normal for \(n \geq 30\)?
5. How can the Central Limit Theorem be used to make inferences about the population from the sample?

**Tip:** The larger your sample size, the closer the sampling distribution of the mean will approximate a normal distribution, even if the population itself is not normally distributed.

The Central Limit Theorem will tell us a few important things: 1) The mean of ALL sampling distributions equals the mean of the population. 2) The standard deviation for a sampling distribution is equal to the population standard deviation divided by the square root of the sample size. 3) For n >= 30, the sampling distribution should be approximately normal. If Population mean = 24.4, Population standard deviation = 6.49, and sample size n = 37, what is the mean of the sampling distribution?

Learn how to calculate the mean of the sampling distribution using the Central Limit Theorem. With a population mean of 24.4 and a sample size of 37, this problem walks through key statistical concepts, including the Central Limit Theorem and sampling distribution properties. Perfect for Grades 11-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation