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 ​$245 and a standard deviation of ​$66. Random samples of size 32 are drawn from this population and the mean of each sample is determined. 
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Part 1
The mean of the distribution of sample means is 
  
245.
Part 2
The standard deviation of the distribution of sample means is 
  

​(Type an integer or decimal rounded to three decimal places as​ needed.)

Here is the graph of the sampling distribution of sample means, centered at $245, with the standard error of $11.67 shown on either side of the mean.

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Here are 5 related questions to expand on this:

1. How does increasing the sample size affect the standard error?
2. What is the difference between the standard deviation of the population and the standard error of the mean?
3. How would the graph change if the standard deviation of the population were higher?
4. What does the Central Limit Theorem say about the shape of the sampling distribution for small sample sizes?
5. How can we use this sampling distribution to calculate confidence intervals for the population mean?

**Tip:** The larger the sample size, the smaller the standard error, making your sample means more precise estimates of the population mean.

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 ​$245 and a standard deviation of ​$66. Random samples of size 32 are drawn from this population and the mean of each sample is determined.

Calculate the mean and standard error of the sampling distribution for photo printer prices, with a population mean of $245 and a standard deviation of $66. Understand how to apply the Central Limit Theorem to determine the distribution of sample means for a sample size of 32. Suitable for undergraduate statistics students.

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