Question: Population \(\mathrm{X}\) consists of the following numerical values and corresponding letter designations:

Let Proportion of Interest \(=\Phi_{\mathrm{A}}\).

1. With replacement, draw all possible samples of size \(\mathrm{n}=3\) and, by relying on sampling distributions, prove the Central Limit Theorem (CLT) for the \(\mu_{\mathrm{X}}\) and \(\Phi_{\mathrm{A}}\).
2. Draw the Sampling Distribution of the Variance (SDV). Show that the SDV's average is equal to the population variance. Draw the SDV's probability distribution and describe its shape.

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