Question

find the mean and standard error of the mean of the sampling distribution. then sketch a graph of the sampling distribution. the prices of photo printers on a website are normally distributed with a mean of $238 and a standard deviation of $55. random samples of size 24 are drawn from this population and the mean of each sample is determined. the mean of the distribution of sample means is 238. the mean of the distribution of sample means is . the standard deviation of the distribution of sample means is (type an integer or decimal rounded to three decimal places as needed.)

Explanation:

Step1: Recall mean of sampling - distribution property

The mean of the sampling - distribution of the sample means ($\mu_{\bar{x}}$) is equal to the population mean ($\mu$). Given $\mu = 238$, so $\mu_{\bar{x}}=238$.

Step2: Recall standard - error formula

The standard error of the mean ($\sigma_{\bar{x}}$) is given by the formula $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard deviation and $n$ is the sample size. Here, $\sigma = 55$ and $n = 24$.
$\sigma_{\bar{x}}=\frac{55}{\sqrt{24}}\approx11.225$

Answer:

The mean of the distribution of sample means is $238$.
The standard deviation of the distribution of sample means (standard error) is approximately $11.225$.