Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary.
\[
\mu=52 \text { and } \sigma=9 ; n=49
\]
Answer

Step 1 ：Given that the standard deviation of the population, \(\sigma\), is 9 and the size of the samples, \(n\), is 49, we can calculate the standard deviation of the sampling distribution of sample means, \(\sigma_{\bar{x}}\), using the formula \(\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}\).

Step 2 ：Substituting the given values into the formula, we get \(\sigma_{\bar{x}} = \frac{9}{\sqrt{49}}\).

Step 3 ：Calculating the above expression, we find that \(\sigma_{\bar{x}}\) is approximately 1.2857142857142858.

Step 4 ：Rounding to one decimal place, we get \(\sigma_{\bar{x}}\) is approximately 1.3.

Step 5 ：Final Answer: The standard deviation of the sampling distribution of sample means is \(\boxed{1.3}\).