Character recognition, again. The automatic character recognition device discussed in Exercise 22 successfully reads about 85% of handwritten loan applications. In Exercise 22 you looked at the histograms showing distributions of sample proportions from 1000 simulated samples of size 20, 50, 75, and 100.

The sample statistics from each simulation were as follows:

n mean st. dev.
20 0.8481 0.0803 50 0.8507 0.0509 75 0.8481 0.0406 100 0.8488 0.0354

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 22, 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?