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 how these histograms change as the sample size increases. Be sure to talk about shape, centre, and spread.

Number of Samples Number of Samples Samples of Size 20 400 300 200 100 0 0.5 Sample Proportions 1.0 Number of Samples 300 200 100 0 T Samples of Size 50 0.65 1.00 Sample Proportions Samples of Size 75 Samples of Size 100 250 200 200- 150 150 100 50- 0 0.65 Sample Proportions Number of Samples 100 50 50 0 1.00 0.75 0.85 0.95 Sample Proportions