Question: If you use statistical software, you can continue the exploration begun in Exercise 4.8. Software allows you to simulate many independent "Yes/No" trials more quickly if all you want to save is the count of "Yes" outcomes. The keyword "Binomial" simulates \(n\) independent Yes/No trials, each with probability \(p\) of a "Yes," and records just the count of "Yes" outcomes.

1. Simulate 100 draws of 20 Internet users from the population in Exercise 4.8. (That is, ask the software to generate 100 binomial observations, each with \(n=20\) trials and probability \(p=0.3\) of a "Yes,") Record the count in the 18 to 29 age group on each draw. Convert the counts into percents of the 20 Internet users in each trial who are 18 to 29. Make a histogram of these 100 percents. Describe the shape, center, and spread of this distribution.
2. Now simulate drawing 320 Internet users. (That is, set \(n=320\) and \(p=\) 0.3.) Do this 100 times and record the percent in the 18 to 29 age group for each of the 100 draws. Make a histogram of the percents and describe the shape, center, and spread of the distribution.
3. In what ways are the distributions in parts (a) and (b) alike? In what ways do they differ? (Because regularity emerges in the long run, we expect the results of drawing 320 subjects to be less variable than the results of drawing 20 subjects.)

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