**Educational Text: Understanding the Sampling Distribution Using the Central Limit Theorem**To explore the central limit theorem, we aim to identify the mean and standard error of the mean for a specific sampling distribution. Subsequently, we will sketch the appropriate graph for this distribution.**Scenario:**The per capita consumption of red meat by individuals in a certain country follows a normal distribution, with an established mean of 115 pounds and a standard deviation of 37.2 pounds. Random samples, each consisting of 15 individuals, are drawn from this population, and the mean for each sample is calculated.**Calculations:**1. **Mean of the Sampling Distribution (\( \mu_{\bar{x}} \)):** - Since the sample mean is an unbiased estimator of the population mean, \( \mu_{\bar{x}} = \mu = 115 \) pounds.2. **Standard Error of the Mean (\( \sigma_{\bar{x}} \)):** - Calculated using the formula \( \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \), where \( \sigma \) is the population standard deviation and \( n \) is the sample size. - \( \sigma_{\bar{x}} = \frac{37.2}{\sqrt{15}} \approx 9.606 \) (rounded to three decimal places).**Graphing the Sampling Distribution:**We are provided with four graph options (A, B, C, D) to sketch the correct sampling distribution:- **Graph A:** The x-axis ranges from -105.4 to 124.6 with a centered mean at 9.6.- **Graph B:** The x-axis spans from -335.4 to 354.6 with a centering point at 9.6.- **Graph C:** The x-axis covers 86.2 to 143.8 with a centered mean at 115.- **Graph D:** The x-axis runs from 95.8 to 134.2 with a centered mean at 115.**Correct Graph:**The appropriate graph should reflect a normal distribution centered at the mean of 115 with a standard error of approximately 9.606. Based on these criteria, **Graph D** represents the correct sampling distribution. It has a centered mean of 115 pounds and reflects the variability (standard error) expected in the sampling distribution.

Mean of the sampling distribution of the sample mean. Standard deviation of the sampling…

Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 115 pounds and a standard deviation of 37.2 pounds. Random samples of size 15 are drawn from this population and the mean of each sample is determined. G: = (Round to three decimal places as needed) Sketch a graph of the sampling distribution. Choose the correct graph below. OA. OB. OC. OD. 86.2 115 1438 958 115 1342 -105.4 9.6 124.6 -335.4 9.6 354.6

Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 115 pounds and a standard deviation of 37.2 pounds. Random samples of size 15 are drawn from this population and the mean of each sample is determined. G: = (Round to three decimal places as needed) Sketch a graph of the sampling distribution. Choose the correct graph below. OA. OB. OC. OD. 86.2 115 1438 958 115 1342 -105.4 9.6 124.6 -335.4 9.6 354.6

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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