Government agencies keep data about the income distribution of the population. The Brown family and Mitchell family live in a county with 11,000 families. The Brown family's Income is at the 36th percentile. The Mitchell family's Income is at the 19th percentile. (a) Which of the following must be true about the Brown family's Income? The Brown family earns about 36% of the highest income in their county. O The Brown family's Income is in the top half of incomes in their county. The Brown family earns $36,000. O The Brown family earns less than about 64% of families in their county. (b) Which of the following must be true about the Brown family's and the Mitchell family's incomes? O The Brown family earns $17,000 more than the Mitchell family. O The Mitchell family earns $17,000 more than the Brown family. Both the Brown family and the Mitchell family earn more than the median Both the Brown family and the Mitchell family earn less than the median O income. Explanation Check hp X ©2022 McGraw Hill LLC. All Rights Reserved. Terms of Use Privacy Center A

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### Understanding Income Percentiles

Government agencies keep data about the income distribution of the population. The Brown family and Mitchell family live in a county with 11,000 families. The Brown family's income is at the 36th percentile. The Mitchell family's income is at the 19th percentile.

#### Questions:

**(a) Which of the following must be true about the Brown family’s income?**

- O The Brown family earns about 36% of the highest income in their county.
- O The Brown family’s income is in the top half of incomes in their county.
- O The Brown family earns $36,000.
- ● The Brown family earns less than about 64% of families in their county.

**(b) Which of the following must be true about the Brown family’s and the Mitchell family’s incomes?**

- O The Brown family earns $17,000 more than the Mitchell family.
- O The Mitchell family earns $17,000 more than the Brown family.
- O Both the Brown family and the Mitchell family earn more than the median income.
- ● Both the Brown family and the Mitchell family earn less than the median income.

Note: The filled circles represent the selected correct answers.

### Explanation:

This exercise helps illustrate how percentiles work in income distribution within a population. It shows the relative standing of two families compared to the rest of the county's families. Percentile ranks express how much of the population earns less than a given family, providing insights into income inequality and economic standing.
Transcribed Image Text:### Understanding Income Percentiles Government agencies keep data about the income distribution of the population. The Brown family and Mitchell family live in a county with 11,000 families. The Brown family's income is at the 36th percentile. The Mitchell family's income is at the 19th percentile. #### Questions: **(a) Which of the following must be true about the Brown family’s income?** - O The Brown family earns about 36% of the highest income in their county. - O The Brown family’s income is in the top half of incomes in their county. - O The Brown family earns $36,000. - ● The Brown family earns less than about 64% of families in their county. **(b) Which of the following must be true about the Brown family’s and the Mitchell family’s incomes?** - O The Brown family earns $17,000 more than the Mitchell family. - O The Mitchell family earns $17,000 more than the Brown family. - O Both the Brown family and the Mitchell family earn more than the median income. - ● Both the Brown family and the Mitchell family earn less than the median income. Note: The filled circles represent the selected correct answers. ### Explanation: This exercise helps illustrate how percentiles work in income distribution within a population. It shows the relative standing of two families compared to the rest of the county's families. Percentile ranks express how much of the population earns less than a given family, providing insights into income inequality and economic standing.
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