The philanthropic organization in Exercise 3 expects about a 5% success rate when they send fundraising letters to the people on their mailing list. In Exercise 3, you looked at the histograms showing distribution of sample proportions from 1000 simulated mailings for samples of size 20, 50, 100, and 200. Here are both the theoretical and observed statistics for these simulated samples:

a) Looking at the histograms of Exercise 3, at what sample size would you be comfortable using the Normal model as an approximation for the sampling distribution?
b) What does the Success/Failure Condition say about the choice you made in part a?

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Observed Theoretical Observed Theoretical Mean Mean st. dev st. dev 20 0.0497 0.05 0.0479 0.0487 50 0.0516 005 0.0309 0.0308 100 0.0497 0.05 0.0215 0.0218 200 0.0501 0.05 0.0152 0.0154 Samples of Size 20 Samples of Size 50 250 200 150 100 300 200 100 2 50 0.00 0.25 0.00 0.15 Sample Proportions Sample Proportions Samples of Size 100 Samples of Size 200 120 100 80 150 그 100 50 6 60- 40- 2 20 0.14 002 0.06 0.10 Sample Proportions 0.00 Sample Proportions