More efficient simulation. Continue the exploration begun in Exercise 4.12. 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 key word “Binomial” simulates n independent Bernoulli trials, each with probability p of a Yes, and records just the count of Yes outcomes.

(a) Simulate 100 draws of 20 people from the population in Exercise 4.12. Record the number who approve of labor unions on each draw. What is the approximate probability that out of 20 people drawn at random at least 14 approve of labor unions?

(b) Convert the “approval” counts into percents of the 20 people in each trial. Make a histogram of these 100 percents. Describe the shape, center, and spread of this distribution.

(c) Now simulate drawing 320 people. Do this 100 times and record the percent who approve on each of the 100 draws. Make a histogram of the percents and describe the shape, center, and spread of the distribution.

(d) In what ways are the distributions in parts

(b) and

(c) alike?
In what ways do they differ? (Because regularity emerges in the long run, we expect the results of drawing 320 individuals many times to be less variable than the results of drawing 20 individuals many times.)