I would appreciate help with the answers to all questions please. Thanks in advance. Question c: looking at the histograms, at what sample size would you be comfortable using the Normal model as an approximation for the sampling distribution? 200,30,100 or 50?Question d: what about the shape of the distribution of Total Compensation explains your choice of sample size in part c?

Researchers studied the compensation of 515 CEOs. The true mean and standard deviation of the CEO compensation in thousands of dollars for the 515 CEOs are 10,304.14 thousand dollars and 17,969.71 dollars, respectively. A research organization simulated sample means by drawing samples of 30, 50, 100, and 200, with replacement, from the 515 CEOs. The accompanying histograms show the distributions of means for many samples of each size, The summary statistics for these n mean st. dev. simulations are shown to the right Complete parts a through d. 30 10,229.33 3344 47 50 10.269.72 2509.49 100 10,315 84 1796.79 200 10,312 71 1270.51 Click the icon to view the original histogram and histograms for the sampling distributions. a) According to the Central Limit Theorem, what should the theoretical mean and standard deviation be for each of these sample sizes? Find the theoretical means Theoretical n mean 30 1 Histograms X 50 100 200 The histogram of the original distribution of CEO compensation is shown to the (Round to two decimal places as needed.) right. 500- 400- a Find the standard deviations. ICEOD 300- n Theoretical 200 st. dev 100 30 150 000 300,000 50 Compensation in $1000 100 The histograms of simulations that drew many samples of sizes 30, 50, 100, and 200 (with replacement) are 200 shown below. (Round to two decimal places as needed.) Samples of size 30 Samples of size 50 Samples of size 100 Sample 300 400- 300- 200- b) Are the theoretical values close to what was observed in the simulation? 300- 200- 200- Number of Samples Number of Samples Number of Samples 200- A. The theoretical values are significantly larger than the simulation values. 100 100 100- ? Click to select your answer(s). 15,000 30.000 0 15,000 30,000 5000 20.000 7000 Sample Mean Compensation Sample Mean Compensation Sample Mean Compensation Sample