The Central Limit Theorem can be demonstrated by taking sample mean distributions from a population that is not normally distributed.Graph the probability distribution for rolling a six-sided die as a relative frequency histogram. Determine the mean and standard deviation for this distribution.Construct a relative frequency distribution for a sample mean distribution with sample size of 4 for rolling a six-sided die using 100 trials. Sketch this as a relative frequency histogram using the same horizontal and vertical scales as the relative frequency histogram for the population. This means using classes of ̅̅ 1 ≤ x ̅ < 2, 2 ≤ x ̅ <3, etc. This can be done using real dice rolls or simulations using random number generators.Determine the mean and standard deviation for the sample mean distribution with n = 4.Repeat the process for the sample mean when n = 9. Graph the relative frequency histogram using the same scale as the previous wo distributions.Enter the mean and standard deviations for all three distributions in the table below. DistributionMeanStandard DeviationPopulation Sample Mean, n=4 Sample Mean, n=9

Given Information: Consider a six-sided die that has possible outcomes1,2,3,4,5,6. The probability…

Answered: The Central Limit Theorem can be…

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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The Central Limit Theorem can be demonstrated by taking sample mean distributions from a population that is not normally distributed.

Graph the probability distribution for rolling a six-sided die as a relative frequency histogram. Determine the mean and standard deviation for this distribution.
Construct a relative frequency distribution for a sample mean distribution with sample size of 4 for rolling a six-sided die using 100 trials. Sketch this as a relative frequency histogram using the same horizontal and vertical scales as the relative frequency histogram for the population. This means using classes of ̅̅ 1 ≤ x ̅ < 2, 2 ≤ x ̅ <3, etc. This can be done using real dice rolls or simulations using random number generators.
Determine the mean and standard deviation for the sample mean distribution with n = 4.

Repeat the process for the sample mean when n = 9. Graph the relative frequency histogram using the same scale as the previous wo distributions.
Enter the mean and standard deviations for all three distributions in the table below.

Distribution	Mean	Standard Deviation
Population
Sample Mean, n=4
Sample Mean, n=9

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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