Question

A national chain of department stores ranks its 1,000,000 salespeople by the monetary value of their sales. Karen's sales are at the 26th percentile. Brian's sales

are at the 33rd percentile.
(If necessary, consult a list of formulas.)

Which of the following must be true about Karen's sales?
A. The value of Karen's sales were about 26% of the chain's total.
B. The value of Karen's sales was in the top half of all of the salespeople.
C. Karen sold $2600 in merchandise.
D. Karen had sales lower in value than about 74% of the salespeople.

Answer 1

Karen's ranking at the 26th percentile means that her sales were greater than or equal to 26% of all salespeople, and lower than about 74% of them. It does not specify her exact sales value or share of the total sales. The correct answer is option D.

Step-by-step explanation:

The student is asking which statement must be true about Karen's sales, given that her sales are at the 26th percentile in a ranking of 1,000,000 salespeople. First, it is important to understand what being at the 26th percentile means. The percentile measures the percentage of scores in a distribution that are equal to or lower than it.

Therefore, being at the 26th percentile means that Karen's sales were equal to or greater than 26% of all salespeople, not that her sales contributed to 26% of the total sales. It also does not imply where she falls within the top or bottom half, or the exact monetary value of her sales.

Given the misunderstanding of percentiles, the correct answer is:
D. Karen had sales lower in value than about 74% of the salespeople. This is because 100% - 26% = 74%, and thus implies that 74% of the salespeople had higher sales than Karen.