=+22. Character recognition. An automatic character recognition device can successfully read about 85% of handwritten credit card applications. To estimate what might happen when this device reads a stack of applications, the company did a simulation using samples of size 20, 50, 75, and 100.

For each sample size, they simulated 1000 samples with success rate p = 0.85 and constructed the histogram of the 1000 sample proportions, shown here. Explain what these histograms say about the sampling distribution model for sample proportions. Be sure to talk about shape, center, and spread.

Sample Proportions Samples of Size 20 Number of Samples 400 300 200 100 0

0.5 1.0 0.65 Sample Proportions Samples of Size 50 1.00 Number of Samples 300 200 100 0

0.65 Sample Proportions Samples of Size 75 1.00 Number of Samples 250 200 150 100 50 0

Sample Proportions Samples of Size 100 0.75 0.85 0.95 Number of Samples 200 150 100 50 0