One growing concern regarding the U.S. economy is the inequality in the distribution of income. The data in Table 1 represent the distribution of household income for various levels of income in 2000. An economist wants to know if the distribution of income is changing, so she randomly selects 1500 households and obtains the household income. Find the expected number of households at each income level assuming that the distribution of income has not changed since 2000.

Note: The income data has been adjusted for inflation.

Approach Any quantitative variable (such as income) can become qualitative when categories of the variable are created. For example, in this data, we have seven categories of income. There are two steps to follow to determine the expected counts for each category.

Step 1 Determine the probabilities for each outcome.

Step 2 There are \(n=1500\) trials (the 1500 households surveyed) of the experiment. We expect \(n p_{\text {under }} \$ 15,000\) of the households surveyed to have an income under \(\$ 15,000\).