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Use the Central Limit Theorem to find the mean and standard error of the mean of...

Use the Central Limit Theorem to find the mean and standard error of the mean of the sampling distribution. Then sketch a graph of the sampling distribution. The mean price of photo printers on a website is ​$228 with a standard deviation of ​$61. Random samples of size 34 are drawn from this population and the mean of each sample is determined. What is the standard deviation of the distribution of sample means ? (Type an integer or decimal rounded to three decimal places as​ needed.)

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Expert Solution

Solution:

Given: The mean price of photo printers on a website is ​$228 with a standard deviation of ​$61.

That is: Mean = and standard deviation =

Sample Size = n = 34

We have to use the Central Limit Theorem to find the mean and standard error of the mean of the sampling distribution.

Since sample size = n = 34 > 30 is large sample, thus using  the Central Limit Theorem, the sampling distribution of sample means is approximately Normal with mean of sample mean is:

and standard deviation of the distribution of sample means is:

Sketch of the sampling distribution:

Thus we get:

milcah answered 1 year ago
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