Problem

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

Solution

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 \(\boxed{1.3}\).

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Source: https://solvelyapp.com/problems/8503/

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