Question

a national chain of department stores ranks its 1,250,000 salespeople by the monetary value of their sales. justins sales are at the 72nd percentile. susans sales are at the 29th percentile.
(a) which of the following must be true about justins sales?
o about 72% of the salespeople had sales lower in value than justin.
o the value of justins sales were about 72% of the chains total.
o the value of justins sales was in the bottom half of all of the salespeople.
o justin sold $7200 in merchandise.
(b) which of the following must be true about justins and susans sales?
o both justin and susan had sales higher in value than the median.
o both justin and susan had sales lower in value than the median.
o justins sales were higher in value than susans sales.
o susans sales were higher in value than justins sales.

Explanation:

Step1: Recall the definition of percentile

If a value is at the \(n\)th percentile, approximately \(n\%\) of the data values are less than or equal to that value.

Step2: Analyze part (a)

Since Justin's sales are at the \(72\)nd percentile, about \(72\%\) of the salespeople had sales lower in value than Justin.

Step3: Analyze part (b)

Susan's sales are at the \(29\)th percentile. The median is the \(50\)th percentile. So Susan's sales were lower in value than the median. Justin's sales are at the \(72\)nd percentile, so Justin's sales were higher in value than the median.

Answer:

(a) About \(72\%\) of the salespeople had sales lower in value than Justin.
(b) Both Justin and Susan had sales higher and lower in value than the median respectively.