Question

government agencies keep data about the income distribution of the population. the tanaka family and bennett family live in a county with 11,000 families. the tanaka familys income is at the 19th percentile. the bennett familys income is at the 61st percentile. (if necessary, consult a list of formulas.) (a) which of the following must be true about the tanaka familys and the bennett familys incomes? both the tanaka family and the bennett family earn more than the median income. both the tanaka family and the bennett family earn less than the median income. the bennett family earns more than the tanaka family. the tanaka family earns more than the bennett family. (b) which of the following must be true about the tanaka familys income? about 19% of the families in their county earn less than the tanaka family. the tanaka family earns about 19% of the highest income in their county. the tanaka familys income is in the top half of incomes in their county. the tanaka family earns $19,000.

Explanation:

Step1: Understand percentile concept

The $n^{th}$ percentile means $n\%$ of the data values are less than or equal to that value.

Step2: Analyze part (a)

The Tanaka family is at the 19th percentile and the Bennett family is at the 61st percentile. Since 19 < 61, the Bennett family has a higher - ranked income. So the Bennett family earns more than the Tanaka family.

Step3: Analyze part (b)

The Tanaka family is at the 19th percentile. By the definition of percentile, about 19% of the families in their county earn less than the Tanaka family.

Answer:

(a) The Bennett family earns more than the Tanaka family.
(b) About 19% of the families in their county earn less than the Tanaka family.