Math  /  Data & Statistics

QuestionGovernment agencies keep data about the income distribution of the population. The Wood family and Butler family live in a county with 11,000 families. The Wood family's income is at the 14th 14^{\text {th }} percentile. The Butler family's income is at the 59th 59^{\text {th }} percentile. (a) Which of the following must be true about the Wood family's and the Butler family's incomes? The Butler family earns more than the Wood family. Both the Wood family and the Butler family earn more than the median income. The Butler family earns $45,000\$ 45,000 more than the Wood family.
The Wood family and the Butler family both have incomes in the bottom half of incomes in their county. (b) Which of the following must be true about the Wood family's income? The Wood family earns more than about 86%86 \% of families in their county. About 86%86 \% of the families in their county earn more than the Wood family. The wood family earns about 14%14 \% of the highest income in their county. The wood family earns about 86%86 \% of the highest income in their county.

Studdy Solution
Analyze the statement: "The Wood family earns about 86%86\% of the highest income in their county."
Percentiles do not provide information about specific income amounts, so this statement cannot be determined to be true based on the given information.
The conclusions are: (a) The only true statement is: "The Butler family earns more than the Wood family." (b) The only true statement is: "About 86%86\% of the families in their county earn more than the Wood family."

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