Score: $32.5 / 100$ $11 / 20$ answered Question 11 A population of values has a normal distribution with $\mu=32.9$ and $\sigma=55.3$. You intend to draw a random sample of size $n=32$. What is the mean of the distribution of sample means? \[ \mu_{x}= \] What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.) \[ \sigma_{x}= \] Question Help: $\square$ Video D Post to forum Submit Question

Step 1 ：Given that the population mean, \(\mu\), is 32.9 and the population standard deviation, \(\sigma\), is 55.3, and the sample size, \(n\), is 32.

Step 2 ：The mean of the distribution of sample means, often denoted as \(\mu_{x}\), is equal to the population mean, \(\mu\). So, \(\mu_{x} = 32.9\).

Step 3 ：The standard deviation of the distribution of sample means, often denoted as \(\sigma_{x}\), is equal to the population standard deviation, \(\sigma\), divided by the square root of the sample size, \(n\). So, \(\sigma_{x} = \sigma / \sqrt{n} = 55.3 / \sqrt{32}\).

Step 4 ：Calculate \(\sigma_{x}\): \(\sigma_{x} = 55.3 / \sqrt{32} \approx 9.77\) (rounded to two decimal places).

Step 5 ：\(\boxed{\mu_{x} = 32.9, \sigma_{x} \approx 9.77}\)