**Question 3: Sampling Distribution of the Sample Mean**A random sample of size $ n $ is selected from a population with a mean of 100 and a standard deviation of 20. Find the mean ($\mu_{\bar{x}}$) and standard deviation ($\sigma_{\bar{x}}$) of the sample mean for each of the following values:a. $ n = 25 $b. $ n = 36 $c. $ n = 64 $d. $ n = 20 $e. In which of these cases can we be assured that the sampling distribution of the sample mean will be approximately normally distributed?**Explanation:**For a sample size $ n $, the mean of the sampling distribution of the sample mean ($\mu_{\bar{x}}$) is equal to the mean of the population, which is 100. The standard deviation of the sampling distribution of the sample mean ($\sigma_{\bar{x}}$) is calculated using the formula:\[\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}\]where $\sigma$ is the standard deviation of the population.The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normally distributed if the sample size $ n $ is sufficiently large, typically $ n \geq 30 $.

3. A random sample of size nis selected from a population with mean 100 and standard deviation 20. Find the mean (µ,) and standard deviation (o, ) of the sample mean for each of the following values. а. n = 25 с. n = 64 b. п3D 36 d. n = 20 e. In which of these cases can we be assured that the sampling distribution of the sample mean will be approximately normally distributed?

3. A random sample of size nis selected from a population with mean 100 and standard deviation 20. Find the mean (µ,) and standard deviation (o, ) of the sample mean for each of the following values. а. n = 25 с. n = 64 b. п3D 36 d. n = 20 e. In which of these cases can we be assured that the sampling distribution of the sample mean will be approximately normally distributed?

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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