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 demonstrate what the Central Limit Theorem says about the sampling distribution model for sample proportions. Be sure to talk about shape, center, and spread.

Number of Samples Number of Samples 250 Samples of Size 20 400 300 300 200 100 0 Number of Samples 200 100 200- 150 100 50- 0 0.65 0.5 Sample Proportions Samples of Size 75 Sample Proportions 0 1.0 0.65 Number of Samples Samples of Size 50 Sample Proportions Samples of Size 100 200 150 00 100 50 0 1.00 0.75 0.85 0.95 Sample Proportions 1.00