Question

a national chain of department stores ranks its 1,000,000 salespeople by the monetary value of their sales. ritas sales are at the 32nd percentile. manuels sales are at the 68th percentile.
(a) which of the following must be true about ritas and manuels sales?
manuels sales were higher in value than ritas sales.
both rita and manuel had sales higher in value than the median.
the value of manuels sales were $3400 more than ritas.
the values of both ritas and manuels sales were in the bottom half of all of the salespeople.
(b) which of the following must be true about ritas sales?
rita had sales higher in value than about 68% of the salespeople.
about 68% of the salespeople had sales higher in value than rita.
the value of ritas sales were about 32% of the chains total.
the value of ritas sales were about 68% of the chains total.

Explanation:

(a)

Step1: Recall the definition of percentile

The \(p^{th}\) percentile means that \(p\%\) of the data is less than or equal to that value. Since \(32<66\), Manuel's sales (at \(66^{th}\) percentile) are higher than Rita's (at \(32^{nd}\) percentile).

Step2: Analyze other options

• Median is the \(50^{th}\) percentile. Rita (\(32^{nd}\)) is below the median.
• There is no information about the actual values of sales, so we can't say the difference in dollars.
• Manuel (\(66^{th}\)) is above the bottom - half (\(50^{th}\) percentile)

(b)

Step1: Recall the definition of percentile

If Rita is at the \(32^{nd}\) percentile, then about \(32\%\) of the salespeople have sales less than or equal to Rita's, and about \((100 - 32)\%=68\%\) of the salespeople have sales higher than Rita's.

Step2: Analyze other options

• Rita is at \(32^{nd}\) percentile, so she has sales higher than about \(32\%\) (not \(68\%\)) of salespeople.
• Percentile is about the rank, not the proportion of the total sales.

Answer:

(a) Manuel’s sales were higher in value than Rita’s sales.
(b) About \(68\%\) of the salespeople had sales higher in value than Rita.