In a study of tax write-offs by the affluent, Peter Dreier of Occidental College (Los Angeles) compiled the relative frequency distribution shown on the right.

The distribution describes the incomes of all households in the United States that filed tax returns in 1995. A household is to be randomly sampled from this population.

a. Explain why the percentages in the table can be interpreted as probabilities. For example, the probability of selecting a household with income under

$10,000 is ,185.

h. Find the probability that the selected household has income over $200,000; over $100,000; less than

$100.000; between $30,000 and $49,999.

c. Together, the income categories (1,2,3,. . .) and the percentages form a discrete probability distribution.

Graph this distribution.

d. What is the probability that the randomly selected household will fall in income category 6? In income category 1 or 9?