**Topic: Sampling Distribution and Central Limit Theorem****Example Problem:**The heights of fully grown trees of a specific species are normally distributed, with a mean (\(\mu\)) of 71.5 feet and a standard deviation (\(\sigma\)) of 7.25 feet. Random samples of size 12 are drawn from the population. **Task:**Use the central limit theorem to find the mean and standard error of the sampling distribution. Then sketch a graph of the sampling distribution.1. **Mean of the Sampling Distribution (\(\mu_{\bar{x}}\)):** The mean of the sampling distribution is the same as the mean of the population: \[ \mu_{\bar{x}} = \mu = 71.5 \] 2. **Standard Error of the Sampling Distribution (\(\sigma_{\bar{x}}\)):** The standard error is the standard deviation of the population divided by the square root of the sample size (\(n\)): \[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{7.25}{\sqrt{12}} \] **Calculate and round to two decimal places as needed.**3. **Graph of the Sampling Distribution:** - Sketch a normal distribution curve centered at 71.5. - Indicate the standard error on the graph to show the spread of the sample means around the population mean. **Instructions:**Enter your answers in the respective fields and click "Check Answer" to verify your calculations.

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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 7.25 feet. Random samples of size 12 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, =

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 7.25 feet. Random samples of size 12 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, =

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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