4. [50 pts] Central Limit Theorem: Finding the smallest sample size Each group of students will be assigned a set of two probability distributions, and, for each of these distributions, will determine the smallest sample size for which the conditions of the CLT are satisfied. Instructions: For each distribution, you must: a. Include the command set.seed(value) as the first line in each R script, where value should be replaced by the group number. b. Simulate 100 samples (m = 100). c. Vary the sample size (n =?) until you find the smallest sample size for which the conditions of the CLT are satisfied. d. Confirm your choice of n by replicating your analysis at least ten times. e. Justify your selection with the use of probability plots, hypothesis tests, and descriptive statistics. Deliverables: For each distribution, you must provide: a. A commented R script b. A minimum of three sets of results: i. Results for 10 replicates on a sample size smaller than the suggested n for which the conditions of the CLT are not yet satisfied ii. Results for 10 replicates on the suggested n for which the conditions of the CLT are satisfied iii. Results for 10 replicates on a sample size larger than the suggested n for which the conditions of the CLT are satisfied c. A thorough interpretation of outputs (probability plots, hypothesis tests, and descriptive statistics) Hint: For each set of results, it is strongly recommended that you combine the information for the descriptive statistics and the hypothesis tests in a table, where each row represents the results for a single replicate. You may use the following table format: Replica n Mean Std Dev Median Min Max Range Skew Kurtosis AD p-value 1 2 3 4 5 6 7 8 9 10