# The Central Limit Theorem can be demonstrated by taking sample me

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 ̅<3,1≤x ̅<2,2≤x ̅<3,  etc. This can be done using real dice rolls or simulations using random number generators. On the TI-84 this can be done by adding four randInt(1, 6, 100) values and then dividing by 4 in the list label.    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 DeviationPopulationSample Mean, n=4Sample Mean, n=9 Write a brief paragraph discussing the similarities and differences between these three distributions and how it relates to the Central Limit Theorem.

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