Questions: A population of values has a normal distribution with μ=236.3 and σ=68.5. You intend to draw a random sample of size n=13. What is the mean of the distribution of sample means? μx̄= What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.) σx̄=

A population of values has a normal distribution with μ=236.3 and σ=68.5. You intend to draw a random sample of size n=13.

What is the mean of the distribution of sample means?

μx̄=

What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.)

σx̄=

Transcript text: A population of values has a normal distribution with $\mu=236.3$ and $\sigma=68.5$. You intend to draw a random sample of size $n=13$. What is the mean of the distribution of sample means? \[ \mu_{\bar{x}}= \] $\square$ What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.) \[ \sigma_{\bar{x}}= \] $\square$

Solution

Solution Steps

Step 1: Mean of the Distribution of Sample Means

The mean of the distribution of sample means, denoted as $ \mu_{\bar{x}} $, is equal to the population mean $ \mu $. Therefore, we have:

\[ \mu_{\bar{x}} = 236.3 \]

Step 2: Standard Deviation of the Distribution of Sample Means

The standard deviation of the distribution of sample means, denoted as $ \sigma_{\bar{x}} $, is calculated using the formula:

\[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \]

Substituting the given values:

\[ \sigma_{\bar{x}} = \frac{68.5}{\sqrt{13}} \approx 19.00 \]

Final Answer

The results are as follows:

Mean of the distribution of sample means: $ \mu_{\bar{x}} = 236.3 $
Standard deviation of the distribution of sample means: $ \sigma_{\bar{x}} = 19.00 $

Thus, the final answers are:

\[ \boxed{\mu_{\bar{x}} = 236.3} \] \[ \boxed{\sigma_{\bar{x}} = 19.00} \]

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