Question 2
of 18 Step 1 of 1
01:13:03
Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary.
\[
\mu=40 \text { and } \sigma=8 ; n=9
\]
Answer 2 Points
Tables
Keypad
Keyboard Shortai

Step 1 ：The standard deviation of the sampling distribution of sample means, also known as the standard error, can be calculated using the formula: \(\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}\) where \(\sigma_{\bar{x}}\) is the standard deviation of the sampling distribution, \(\sigma\) is the standard deviation of the population, and \(n\) is the size of the samples.

Step 2 ：Given that \(\sigma = 8\) and \(n = 9\), we can substitute these values into the formula to find \(\sigma_{\bar{x}}\).

Step 3 ：\(\sigma_{\bar{x}} = \frac{8}{\sqrt{9}} = 2.6666666666666665\)

Step 4 ：Rounding to one decimal place, the final answer is: \(\boxed{2.7}\)