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.

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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