**Educational Exercise: Analysis of Sampling Distribution Using the Central Limit Theorem**The exercise focuses on the heights of fully grown trees of a specific species, which are normally distributed. Given data includes:- Mean ($\mu$) = 50.5 feet- Standard deviation ($\sigma$) = 7.25 feet- Sample size = 17**Task Objective:**1. **Calculate the Mean of the Sampling Distribution ($\mu_{\overline{x}}$):** The mean of the sampling distribution is the same as the population mean. Therefore, $\mu_{\overline{x}} = 50.5$ feet.2. **Calculate the Standard Error of the Sampling Distribution ($\sigma_{\overline{x}}$):** The standard error ($\sigma_{\overline{x}}$) is calculated using the formula: \[ \sigma_{\overline{x}} = \frac{\sigma}{\sqrt{n}} \] \[ \sigma_{\overline{x}} = \frac{7.25}{\sqrt{17}} \] Calculate this value and round it to two decimal places.3. **Choose the Correct Graph of the Sampling Distribution:** Three options are provided: - **Option A:** A graph with a standard normal distribution ranging from -2 to 2. - **Option B:** A graph centered at 50.5, with the range approximately from 47 to 54. - **Option C:** A graph centered at 50.5, with a wider range from 36 to 65. To determine the correct graph, compare the calculated mean and standard error with the visual representation of each graph.Upon completing the calculations, select the graph that accurately represents the sampling distribution of the tree heights for samples of size 17.**Answer Key:**- $\mu_{\overline{x}}$ = 50.5- $\sigma_{\overline{x}}$ = (calculated value rounded to two decimals)- Correct graph: B (centered at 50.5, appropriate range)*Choose the graph option that matches your calculations to complete this exercise on sampling distributions.*

Determine the mean of the sampling distribution The mean of the sampling distribution is obtained below as follows: The value of sample mean of the sampling distribution is, Thus, the value of sample mean of the sampling distribution is 50.5.Determine the standard error of the sampling distribution. The standard error of the sampling distribution is obtained below as follows: The standard error of the sampling distribution is Sketch the graph the sampling distribution. The graph of the sampling distribution is obtained below as follows: Correct option: Option B

Math

Statistics

The heights of fully grown trees of a specific species are normally distributed, with a mean of 50.5 feet and a standard deviation of 7.25 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 p; = The standard error of the sampling distribution is o; = (Round to two decimal places as needed.) Choose the correct graph of the sampling distribution below. O A. O B. OC. 47.0 50.5 54.0 36.0 50.5 65.0

The heights of fully grown trees of a specific species are normally distributed, with a mean of 50.5 feet and a standard deviation of 7.25 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 p; = The standard error of the sampling distribution is o; = (Round to two decimal places as needed.) Choose the correct graph of the sampling distribution below. O A. O B. OC. 47.0 50.5 54.0 36.0 50.5 65.0

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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