Send money, again. The philanthropic organization in Exercise 21 expects about a 5% success rate when they send fundraising letters to the people on their mailing list. In Exercise 21 you looked at the histograms showing distributions of sample proportions from 1000 simulated mailings for samples of size 20, 50, 100, and 200.

The sample statistics from each simulation were as follows:

n mean st. dev.
20 0.0497 0.0479 50 0.0516 0.0309 100 0.0497 0.0215 200 0.0501 0.0152

a) According to the Normal model, what should the theoretical mean and standard deviations be for these sample sizes?

b) How close are those theoretical values to what was observed in these simulations?

c) Looking at the histograms in Exercise 21, at what sample size would you be comfortable using the Normal model as an approximation for the sampling distribution?

d) What does the Success/Failure Condition say about the choice you made in part c?