Questions: Correct Suppose a random sample of 36 measurements is selected from a population with mean 67 and standard deviation 12 Step 2 of 2: Find the standard deviation of the sampling distribution of sample means using the given information. Round to two decimal place, if necessary.

Solution Steps

We have a population with the following parameters:

• Population Mean (\( \mu \)): 67
• Population Standard Deviation (\( \sigma \)): 12
• Sample Size (\( n \)): 36

The standard error of the mean (SEM) is calculated using the formula:

\[ SEM = \frac{\sigma}{\sqrt{n}} \]

Substituting the given values:

\[ SEM = \frac{12}{\sqrt{36}} = \frac{12}{6} = 2 \]

The standard error of the mean is already a whole number, so rounding to two decimal places gives:

\[ SEM \approx 2.00 \]

Final Answer