  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 \$244 with a standard deviation of \$63. Random samples of size 29 are drawn from this population and the mean of each sample is determined. 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.)

Question
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 \$244 with a standard deviation of \$63. Random samples of size 29 are drawn from this population and the mean of each sample is determined.

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.)

Step 1

Central Limit Theorem for mean:

If a random sample of size n is taken from a population having mean  and standard deviation  then, as the sample size increases, the sample mean approaches the normal distribution with mean  and standard deviation σ/sqrt(n). The standard deviation obtained is same as the standard error.

Step 2

Computing mean and standard deviation of the distribution of sample mean:

The random variable X denotes price of photo printers on a website. The random variable X follows a distribution with mean \$244 and standard deviation \$63. The sample size is 29. Therefore, from the central limit theorem it is clear that mean price of photo printers on a website follows normal distribution with mean \$244 and standard deviation is 63/sqrt(29) =11.699.  The standard error is 11.699.Therefore,

Step 3

Thus,

The mean of the distribution of sample mean is \$244.

The standard deviation of the distribution of sa...

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