Question

a national chain of department stores ranks its 750,000 salespeople by the monetary value of their sales. chriss sales are at the 96th percentile. lucys sales are at the 75th percentile.
(a) which of the following must be true about chriss sales?
chris had sales lower in value than about 96% of the salespeople.
the value of chriss sales were about 96% of the chains total.
chris had sales higher in value than about 96% of the salespeople.
the value of chriss sales were about 4% of the chains total.
(b) which of the following must be true about chriss and lucys sales?
lucys sales were higher in value than chriss sales.
both chris and lucy had sales higher in value than the median.
the value of chriss sales were $2100 more than lucys.
the values of both chriss and lucys sales were in the bottom half of all of the salespeople.

Explanation:

(a)

Step1: Understand percentile concept

A percentile \( p \) means that approximately \( p\%\) of the data is less than the value at that percentile. If Chris's sales are at the \(96^{th}\) percentile, it means about \(96\%\) of the salespeople had sales lower in value than Chris's.

(b)

Step1: Analyze median and percentile relationship

The median is the \(50^{th}\) percentile. Chris is at \(96^{th}\) percentile (high - value sales) and Lucy is at \(75^{th}\) percentile. Since \(96>75\), Lucy's sales were higher in value than the median (because \(75 > 50\)), and Chris's sales were also higher than the median.

Answer:

(a) Chris had sales lower in value than about \(96\%\) of the salespeople.
(b) Both Chris and Lucy had sales higher in value than the median.