15. Send money. When they send out their fundraising letter, a philanthropic organization typically gets a return from about 5% of the people on their mailing list. To see what the response rate might be for future appeals, they did a simulation using samples of size 20, 50, 100, and 200. For each sample size, they simulated 1000 mailings with success rate p = 0.05 and constructed the histogram of the 1000 sample proportions, shown below. Explain how these histograms demonstrate what the Central Limit Theorem says about the sampling distribution model for sample proportions. Be sure to talk about shape, center, and spread.

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300 Number of Samples 100 100 200 Number of Samples 150- T 1100 100 50 T 0.00 Samples of Size 20 250 Number of Samples 200 150 100 50 Samples of Size 50 0.25 0.00 0.15 Sample Proportions Sample Proportions Samples of Size 100 0.00 Sample Proportions Samples of Size 200 120 Number of Samples 40 20 T 60 T 282 100 80 0 0.14 0.02 0.06 0.10 Sample Proportions