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 four 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.

STAT 2004 WEEK 13 Central limit theorem- No matter the observation distribution, for a large n, x bar ~ N (mu, standard error.) (x bar follows a normal distribution) o This math won’t be tested, but the concept is important. T-distribution- Has more outliers. Handle problems the same way you would handle a normal distribution, but use the t-table chart. o Degrees of freedom- How many pieces of info It is equal to n-1, and follows the t when written in distribution. For example, if it had 7 degrees of freedom the distribution would be written as t17(mu, S.E.). The rest of the lecture was essentially going over the hypotheses again. If you are still hav