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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