Question

(a) which of the following must be true about the young familys and the collins familys incomes?
o the young family earns $17,000 more than the collins family.
o the collins family earns $17,000 more than the young family.
o both the young family and the collins family earn more than the median income.
o both the young family and the collins family earn less than the median income.
(b) which of the following must be true about the young familys income?
o the young family earns about 36% of the highest income in their county.
o the young familys income is in the top half of incomes in their county.
o the young family earns $36,000.
o the young family earns less than about 64% of families in their county.

Explanation:

Step1: Understand percentile concept

A percentile \(p\) means that \(p\%\) of the data values are less than or equal to that value. The Young family is at the \(36^{th}\) percentile. So, \(36\%\) of families have income less than or equal to the Young family's income. Then, \(100 - 36=64\%\) of families have income greater than the Young family's income.

Step2: Analyze each option

• Option 1: The Young family earns \(S36,000\). There is no information given to support this specific income value.
• Option 2: The Young family's income is in the top half of incomes. Since \(36^{th}\) percentile is less than \(50^{th}\) (median), it is not in the top - half.
• Option 3: The Young family earns about \(36\%\) of the highest income. There is no basis for this percentage - of - highest - income claim.
• Option 4: The Young family earns less than about \(64\%\) of families in their county. Since \(36^{th}\) percentile, \(64\%\) of families have higher income.

Answer:

The Young family earns less than about \(64\%\) of families in their county.