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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