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Answer:
To find the standard deviation of the sampling distribution (also known as the standard error of the mean), you use the following formula:
\[ \text{Standard Error (SE)} = \frac{\sigma}{\sqrt{n}} \]
where:
- \(\sigma\) is the population standard deviation
- \(n\) is the sample size
Given:
- Population standard deviation (\(\sigma\)) = 25
- Sample size (\(n\)) = 20
Now, plug in the values:
\[ \text{SE} = \frac{25}{\sqrt{20}} \]
First, calculate \(\sqrt{20}\):
\[ \sqrt{20} \approx 4.47 \]
Then, divide 25 by 4.47:
\[ \text{SE} \approx \frac{25}{4.47} \approx 5.59 \]
So, the standard deviation of the sampling distribution is approximately 5.59.