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.) $$ \sigma_{x}=\square $$

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1. The mean of the sampling distribution of the sample means is equal to the population mean:
   
   $$
   \mu_{x} = 204.2
   $$

2. The standard deviation of the sampling distribution of the sample means (also known as the standard error) is calculated using:
   
   $$
   \sigma_{x} = \frac{\sigma}{\sqrt{n}}
   $$
   
   Plugging in the values:
   
   $$
   \sigma_{x} = \frac{24.3}{\sqrt{184}}
   $$
   
   First, compute $$\sqrt{184}$$:
   
   $$
   \sqrt{184} \approx 13.5647
   $$
   
   Now, calculate $$\sigma_{x}$$:
   
   $$
   \sigma_{x} \approx \frac{24.3}{13.5647} \approx 1.79
   $$

Final Answers:

$$
\mu_{x} = 204.2 \quad \text{and} \quad \sigma_{x} = 1.79
$$
The mean of the distribution of sample means is 204.2, and the standard deviation is 1.79.

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