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 standard deviation of the distribution of sample means is . (type an integer or decimal rounded to three decimal places as needed)

Explanation:

Step1: Recall the formula for standard error

The formula for the standard error of the mean $\sigma_{\bar{x}}$ is $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard - deviation and $n$ is the sample size.

Step2: Identify the values of $\sigma$ and $n$

Given that $\sigma = 55$ (population standard deviation) and $n = 24$ (sample size).

Step3: Calculate the standard error

$\sigma_{\bar{x}}=\frac{55}{\sqrt{24}}\approx\frac{55}{4.899}\approx11.227$

Answer:

11.227