Chapter 2, Problem 39SE

U.S. Distribution of wealth (Example 8) Michael Norton (of Harvard) and Dan Ariely (of Duke) did a survey reported in Harvard Magazine (Nov-Dec 2011). They asked respondents to estimate how much of the wealth is held by each quintile (fifth) of the people in the United States. The top quintile is wealthiest $20\%$ of the people in the people in the United States, and the bottom quintile is the poorest $20\%$ They also asked respondents what the distribution should be ideally. The bar chart shows these responses, well as the true value. For instance, the true value for the bottom fifth is $0.1\%$ and the true value for the fourth fifth is $0.2\%,$ so they are hard to see on the chart. This means that the poorest fifth of the people have only $0.1\%$ of the country’s wealth.)

a. In truth, the top fifth (in terms of wealth) actually held about what percentage of the wealth?

b. Which figures (Ideal, Estimate, or Truth) show the least variation?

c. Which figures (Ideal, Estimate, or Truth) show the most variation?

d. Do people making estimates tend to underestimate or to overestimate the proportion of wealth held by top $20\%?$