Question

a national chain of department stores ranks its 1,000,000 salespeople by the monetary value of their sales. ravis sales are at the 68th percentile. donnas sales are at the 42nd percentile.
(if necessary, consult a list of formulas.)
(a) which of the following must be true about ravis and donnas sales?
ravis sales were higher in value than donnas sales.
both ravi and donna had sales higher in value than the median.
the value of ravis sales were $2600 more than donnas.
the values of both ravis and donnas sales were in the bottom half of all of the salespeople.
(b) which of the following must be true about ravis sales?
ravi had sales higher in value than about 32% of the salespeople.
about 32% of the salespeople had sales higher in value than ravi.
the value of ravis sales were about 68% of the chains total.
the value of ravis sales were about 32% of the chains total.

Explanation:

(a)

Step1: Recall percentile concept

A \(p^{th}\) percentile means \(p\%\) of the data is less than or equal to that value. Since \(68>42\), Ravi's sales (at \(68^{th}\) percentile) are higher than Donna's (at \(42^{nd}\) percentile).

Step2: Analyze other options

• Median is \(50^{th}\) percentile. Donna (\(42^{nd}\)) is below median.
• No info about actual sales difference (\(2600\) claim is baseless).
• Ravi (\(68^{th}\)) is above bottom - half (\(<50^{th}\)).

(b)

Step1: Recall percentile interpretation

If Ravi is at \(68^{th}\) percentile, then \(68\%\) of salespeople have sales less than or equal to Ravi. So, \(100 - 68=32\%\) of salespeople have sales higher than Ravi.

Step2: Analyze other options

• Percentile is about rank, not proportion of total sales (last two options wrong).
• Ravi is higher than \(68\%\) (not \(32\%\)) of salespeople (first option wrong).

Answer:

(a) Ravi’s sales were higher in value than Donna’s sales.
(b) About \(32\%\) of the salespeople had sales higher in value than Ravi.