The heights of fully grown trees of a specific species are normally distributed, with a mean of 71.5 feet and a standard deviation of 6.75 feet. Random samples of size 17 are drawn from the population. Use the central limit theorem to find the mean and standard error of the sampling distribution. Then sketch a graph of the sampling distribution. The mean of the sampling distribution is $\mu_{\bar{x}}=$ The standard error of the sampling distribution is $\sigma_{\bar{x}}=$ (Round to two decimal places as needed)

Step 1 ：The heights of fully grown trees of a specific species are normally distributed, with a mean of 71.5 feet and a standard deviation of 6.75 feet. Random samples of size 17 are drawn from the population.

Step 2 ：According to the central limit theorem, the mean of the sampling distribution is the same as the mean of the population. Therefore, the mean of the sampling distribution is \(\mu_{\bar{x}} = 71.5\) feet.

Step 3 ：The standard error of the sampling distribution is the standard deviation of the population divided by the square root of the sample size. In this case, the standard deviation is 6.75 feet and the sample size is 17.

Step 4 ：Calculate the standard error using these values: \(\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{6.75}{\sqrt{17}}\)

Step 5 ：After calculating, we find that the standard error of the sampling distribution is approximately 1.64 (rounded to two decimal places).

Step 6 ：Finally, we can plot a normal distribution with the calculated mean and standard error. The graph of the sampling distribution is a normal distribution centered at 71.5 with a standard deviation of 1.64.

Step 7 ：Final Answer: The mean of the sampling distribution is \(\boxed{71.5}\) and the standard error of the sampling distribution is \(\boxed{1.64}\) (rounded to two decimal places).