1 2 3 4 5 6 7 8 9 10 Government agencies keep data about the income distribution of the population. The Watson family and waker farnily live in a county with son0 farlies. Toe Watson family's income is at the \( 29^{\text {th }} \) percentile. The Walker family's incerme is at the \( 44^{\text {th }} \) percentile. (a) Which of the following must be true about the Watson family's and the Walker family's incomes? The Walker farnily earns \( \$ 15,000 \) more than the Watson family. The Watson family earns \( \$ 15,000 \) more than the Waliker family. Both the Watson family and the Walker famlly earn more than the median income. Both the Watson family and the Walker family earn less than the median income. (b) Which of the following must be true about the Watson famlly's income? The Watson family earns about \( 29 \% \) of the highest income in their county. The Watson family's income is in the top half of incomes in their county. The Watson farnlly earns \( \$ 29,000 \). The Watson family earns less than about \( 71 \% \) of families in their county.

**(a) Comparison of the Watson and Walker families** - The Watson family is at the \(29^\text{th}\) percentile. This means that approximately \(29\%\) of families earn less than the Watson family, and about \(71\%\) earn more. - The Walker family is at the \(44^\text{th}\) percentile. This means that approximately \(44\%\) of families earn less than the Walker family, and about \(56\%\) earn more. - The median income corresponds to the \(50^\text{th}\) percentile. - Since both \(29 < 50\) and \(44 < 50\), both families earn less than the median income. Thus, the only statement that must be true is that **both the Watson family and the Walker family earn less than the median income**. --- **(b) Statement about the Watson family’s income** - Being at the \(29^\text{th}\) percentile means that the Watson family's income is greater than the incomes of about \(29\%\) of families. - Equivalently, it means that approximately \(71\%\) of the families in the county earn more than the Watson family. - Therefore, the correct interpretation is that **the Watson family earns less than about \(71\%\) of families in their county**. --- **Final Answers:** - (a) Both the Watson family and the Walker family earn less than the median income. - (b) The Watson family earns less than about \(71\%\) of families in their county.