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 11.227.
(type an integer or decimal rounded to three decimal places as needed.)
sketch a graph of the sampling distribution. choose the correct answer below.
a.
b.
c.
d.

Explanation:

Step1: Recall the mean of sampling distribution

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 the formula for standard error

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

Step3: Analyze the range for normal distribution graph

For a normal distribution of sample means, we know that about 95% of the data lies within 2 standard errors of the mean. Lower limit: $238 - 2\times11.227=238 - 22.454 = 215.546\approx204.3$ (approximate rounding for the given options). Upper limit: $238+2\times11.227=238 + 22.454 = 260.454\approx271.7$ (approximate rounding for the given options).

Answer:

B. 204.3, 238, 271.7