**Instruction: Understanding Sampling Distributions**The heights of fully grown trees of a specific species are normally distributed, with a mean of 66.5 feet and a standard deviation of 6.00 feet. Random samples of size 16 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}} = \, \_\_\_ $.*(Round to two decimal places as needed.)***Explanation:**1. **Mean of the Sampling Distribution ($ \mu_{\bar{x}} $):** The mean of the sampling distribution ($ \mu_{\bar{x}} $) is equal to the mean of the population. Therefore, $ \mu_{\bar{x}} = 66.5 $ feet.2. **Standard Error of the Sampling Distribution ($ \sigma_{\bar{x}} $):** The standard error of the sampling distribution is calculated using the formula: \[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \] where $ \sigma = 6.00 $ feet and $ n = 16 $. Substitute these values into the formula and round to two decimal places.3. **Graph of the Sampling Distribution:** - Sketch a normal distribution curve, as the central limit theorem dictates that the sampling distribution of the sample mean will be approximately normally distributed if the sample size is sufficiently large (even if the population distribution is not normal). - Indicate the mean on the graph, as well as the standard error intervals to show the spread of the distribution.**Note:** Ensure all calculations are checked for accuracy.

The following information has been provided: Let X be a random variable that represents the heights…

The heights of fully grown trees of a specific species are normally distributed, with a mean of 66.5 feet and a standard deviation of 6.00 feet. Random samples of size 16 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 p The standard error of the sampling distribution is o (Round to two decimal places as needed.)

The heights of fully grown trees of a specific species are normally distributed, with a mean of 66.5 feet and a standard deviation of 6.00 feet. Random samples of size 16 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 p The standard error of the sampling distribution is o (Round to two decimal places as needed.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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