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.

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.