A population of values has a normal distribution with \( \mu=204.2 \) and \( \sigma=24.3 \). You intend to draw a random sample of size \( n=184 \). What is the mean of the distribution of sample means? \( \mu_{x}=\square \) What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.) \( \sigma_{x}=\square \)

1. The distribution of sample means has the same mean as the population. Thus, \[ \mu_{x} = 204.2. \] 2. The standard deviation of the sample means (also known as the standard error) is given by \[ \sigma_{x} = \frac{\sigma}{\sqrt{n}}. \] Substituting the given values, \[ \sigma_{x} = \frac{24.3}{\sqrt{184}}. \] 3. First, calculate \(\sqrt{184}\): \[ \sqrt{184} \approx 13.56466. \] 4. Then, \[ \sigma_{x} \approx \frac{24.3}{13.56466} \approx 1.79. \] The final answers are: \[ \mu_{x} = 204.2 \quad \text{and} \quad \sigma_{x} = 1.79. \]