Question
A national chain of department stores ranks its 750,000 salespeople by the monetary value of their sales. Reuben's sales are at the \( 73^{\text {rd }} \) percentile. Amanda's sales are at the \( 38^{\text {th }} \) percentile. (If necessary, consult a list of formulas.) (a) Which of the following must be true about Reuben's sales? O About \( 73 \% \) of the salespeople had sales lower in value than Reuben. The value of Reuben's sales were about \( 73 \% \) of the chain's total. The value of Reuben's sales was in the bottom half of all of the salespeople. Reuben sold \( \$ 7300 \) in merchandise. Both Reuben and Amanda had sales higher in value than the median. Both Reuben and Amanda had sales lower in value than the median. Reuben's sales were higher in value than Amanda's sales. (b) Which of the following must be true about Reuben's and Amanda's sales? Ams sales were higher in value than Reuben's sales.
Ask by Warren Johnston. in the United States
Mar 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(a) About 73% of the salespeople had sales lower than Reuben, and Reuben's sales were higher than Amanda's.
(b) Amanda’s sales were not higher than Reuben’s.
Solution
1. We are told that Reuben’s sales are at the \(73^{\text{rd}}\) percentile. By definition, being at the \(73^{\text{rd}}\) percentile means that approximately \(73\%\) of the salespeople had lower sales than Reuben.
2. Amanda’s sales are at the \(38^{\text{th}}\) percentile. This tells us that about \(38\%\) of the salespeople had lower sales than Amanda.
3. Comparing percentiles, since \(73 > 38\), Reuben’s sales are higher in value than Amanda’s sales.
Now we address each part:
(a) Which of the following must be true about Reuben’s sales?
- “About \(73\%\) of the salespeople had sales lower in value than Reuben.”
This is exactly what the \(73^{\text{rd}}\) percentile means, so it must be true.
- “Reuben’s sales were higher in value than Amanda’s sales.”
Since Amanda is at the \(38^{\text{th}}\) percentile and Reuben is at the \(73^{\text{rd}}\) percentile, Reuben’s sales are indeed higher than Amanda’s.
The other statements (such as his sales being about \(73\%\) of the chain’s total, being in the bottom half, or an actual dollar amount like \(\$7300\), etc.) are not necessarily true based solely on the percentile information.
(b) Which of the following must be true about Reuben’s and Amanda’s sales?
- “Amanda’s sales were higher in value than Reuben’s sales.”
This cannot be true because Amanda’s percentile (\(38^{\text{th}}\)) is lower than Reuben’s (\(73^{\text{rd}}\)). Thus, Amanda’s sales must be lower, not higher, than Reuben’s.
In summary:
- For (a), the true statements are:
- About \(73\%\) of the salespeople had sales lower than Reuben.
- Reuben’s sales were higher in value than Amanda’s sales.
- For (b), the statement given (“Amanda’s sales were higher in value than Reuben’s sales”) is not true.
Answered by UpStudy AI and reviewed by a Professional Tutor
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The Deep Dive
About \( 73 \% \) of the salespeople had sales lower in value than Reuben. Being in the \( 73^{\text {rd }} \) percentile, Reuben's sales place him above a significant majority of his peers, indicating that he is quite a star in the sales department! Reuben's sales were higher in value than Amanda's sales. Since Reuben is in the \( 73^{\text {rd }} \) percentile and Amanda is at the \( 38^{\text {th }} \) percentile, it means that Reuben's performance outpaces Amanda's by a considerable margin, making him a competitive force in the department store chain!