Question

a national chain of department stores ranks its 1,000,000 salespeople by the monetary value of their sales. marys sales are at the 16th percentile. michaels sales are at the 88th percentile. (if necessary, consult a list of formulas.) (a) which of the following must be true about marys sales? mary had sales higher in value than about 84% of the salespeople. about 84% of the salespeople had sales higher in value than mary. the value of marys sales were about 16% of the chains total. the value of marys sales were about 84% of the chains total. (b) which of the following must be true about marys and michaels sales? michaels sales were higher in value than marys sales. both mary and michael had sales higher in value than the median. the value of michaels sales were $7200 more than marys. the values of both marys and michaels sales were in the bottom - half of all of the salespeople.

Explanation:

Step1: Recall percentile definition

The $p^{th}$ percentile of a data - set is a value such that $p$ percent of the data values are less than or equal to that value.

Step2: Analyze Mary's percentile (a)

Mary is at the $16^{th}$ percentile. This means that 16% of the salespeople have sales values less than or equal to Mary's, and $100 - 16=84$% of the salespeople have sales higher in value than Mary.

Step3: Analyze Mary and Michael's percentiles (b)

The median is at the $50^{th}$ percentile. Mary is at the $16^{th}$ percentile and Michael is at the $88^{th}$ percentile. Since $88>16$, Michael's sales were higher in value than Mary's sales.

Answer:

(a) About 84% of the salespeople had sales higher in value than Mary.
(b) Michael's sales were higher in value than Mary's sales.