MATH1127: Introduction to Statistics (60022) Unit 3 Test Practice Quizzes Quiz: Chapter 7 uiz: Chapter 7 : $0 / 30 \quad 0 / 6$ answered Question 1 A population has parameters $\mu=245.5$ and $\sigma=71$. You intend to draw a random sample of size $n=91$. What is the mean of the distribution of sample means? $\mu_{\mathrm{x}}=$ What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.) \[ \sigma_{\bar{x}}= \] Check Answer

Step 1 ：The population has parameters \(\mu=245.5\) and \(\sigma=71\). A random sample of size \(n=91\) is drawn.

Step 2 ：The mean of the distribution of sample means, also known as the expected value of the sample mean, is equal to the population mean. This is a property of the Central Limit Theorem. So, in this case, the mean of the distribution of sample means is \(\mu = 245.5\).

Step 3 ：The standard deviation of the distribution of sample means, also known as the standard error, is equal to the population standard deviation divided by the square root of the sample size. This is also a property of the Central Limit Theorem. So, in this case, the standard deviation of the distribution of sample means is \(\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{71}{\sqrt{91}}\).

Step 4 ：Calculating the standard deviation of the distribution of sample means gives \(\sigma_{\bar{x}} = 7.44282234072562\).

Step 5 ：Rounding to two decimal places, the standard deviation of the distribution of sample means is \(\sigma_{\bar{x}} = 7.44\).

Step 6 ：Final Answer: The mean of the distribution of sample means is \(\boxed{245.5}\) and the standard deviation of the distribution of sample means is \(\boxed{7.44}\).