Certainly! Here is the transcription with an educational context:---**Understanding the Central Limit Theorem****Question 14**The Central Limit Theorem states that the sampling distribution of a sample mean, $ \bar{x} $, is approximately normal for:- **a.** random samples taken from populations not known to be Normal if the sample size is large enough- **b.** The Central Limit Theorem states that the sampling distribution of the sample mean can never be approximated by a Normal Model- **c.** only random samples taken from populations that follow a Normal Model- **d.** small, biased samples taken from skewed populations> **Note:** Selecting another question will save your response.**Explanation:**The Central Limit Theorem is a fundamental principle in statistics that enables us to make inferences about population parameters even when the population distribution is not normal. When you take random samples and the sample size is sufficiently large, the distribution of the sample mean tends to be normal, regardless of the shape of the population distribution. This is crucial for conducting hypothesis tests and constructing confidence intervals.In this problem, the most accurate statement is **a**, indicating that for random samples from any population, the sample mean's distribution becomes approximately normal as the sample size increases.---

Solution: Central limit theorem: If the size of the samples taken from the population are sufficiently large (>30) then the mean of all the samples taken would be approximately same as the population mean. Also the sampling distribution would be approximately normal. The population is normal The sample size is greater than 30. If the sample size is large greater than 30, the sampling distribution of sample mean is always approximated to normal.Identify the correct option that best describes the central limit theorem. The correct option is identified below as follows : Reason for the correct option: By, the concept of central limit theorem, it is clear that the sampling distribution of sample mean can be approximated to normal distribution if the sample is large in-spite of the parent population being non-normal because the sample is large. Correct option: Option a Reason for incorrect options: The option b, c and d are incorrect because the sampling distribution can be approximated to normal if sample is large or parent population follows normality and moreover the small samples taken from the skewed populations cannot be approximated to normal.

Math

Statistics

The Central Limit Theorem states that the sampling distribution of a sample mean, y, is approximately normal for O a. random samples taken from populations not known to be Normal if the sample size is large enough O b. The Central Limit Theorem states that the sampling distribution of the sample mean can never be approximated by a Normal Model Oc. only random samples taken from populations that follow a Normal Model O d. small, biased samples taken from skewed populations resnonse

The Central Limit Theorem states that the sampling distribution of a sample mean, y, is approximately normal for O a. random samples taken from populations not known to be Normal if the sample size is large enough O b. The Central Limit Theorem states that the sampling distribution of the sample mean can never be approximated by a Normal Model Oc. only random samples taken from populations that follow a Normal Model O d. small, biased samples taken from skewed populations resnonse

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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