The automatic character recognition device discussed in Exercise 4 successfully reads about 85% of handwritten credit card applications. In Exercise 4, you looked at the histograms showing distributions of sample proportions from 1000 simulated samples of size 20, 50, 75, and 100. The sample statistics and theoretical values for each simulation are as follows:

a) Looking at the histograms in Exercise 4, 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?

Observed Theoretical Observed Theoretical Mean Mean st.dev. st.dev 20 08481 0.85 0.08030.0799 50 0.8507 0.85 0.0509 0.0505 100 0.8481 0.85 0.0406 0.0412 200 0.8488 0.85 00354 0.0357 Samples of Size 20 Samples of Size 50 400 300 300 200 100 100 0.5 1.0 0.65 1,00 Sample Proportions Sample Proportions Samples of Size 75 Samples of Size 100 250 200 150 100 2 50 150 100 S 50 0.65 0.75 0.85 0.95 Sample Proportions 1.00 Sample Proportions