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Answer :
- Week 1's soccer ball purchase percentage is consistent with the model.
- Week 2's soccer ball purchase percentage is inconsistent with the model.
- Week 3's soccer ball purchase percentage is consistent with the model.
- The total soccer ball purchase percentage across all weeks is inconsistent with the model.
$\boxed{{\begin{tabular}{|c|c|}
\hline Consistent with Model & Inconsistent with Model \\
\hline Week 1 results, Week 3 results & Week 2 results, Total of all 3 weeks' results \\
\hline
\end{tabular}}}$
### Explanation
1. Analyze the problem and data
First, we need to calculate the percentage of customers who bought soccer balls for each week and for the total of all three weeks. The model predicts that 58% of customers buy soccer balls. We will classify each result as consistent or inconsistent based on how close the calculated percentage is to 58%. Let's define 'close to' as within 5 percentage points (i.e., between 53% and 63%).
2. Week 1 Analysis
For Week 1:
Total purchases = 85 (soccer balls) + 30 (baseball bats) + 31 (tennis rackets) = 146
Percentage of soccer balls = (85 / 146) * 100 ≈ 58.22%
Since 58.22% is within our defined range of 53% to 63%, Week 1 is consistent with the model.
3. Week 2 Analysis
For Week 2:
Total purchases = 110 (soccer balls) + 22 (baseball bats) + 23 (tennis rackets) = 155
Percentage of soccer balls = (110 / 155) * 100 ≈ 70.97%
Since 70.97% is outside our defined range of 53% to 63%, Week 2 is inconsistent with the model.
4. Week 3 Analysis
For Week 3:
Total purchases = 64 (soccer balls) + 21 (baseball bats) + 23 (tennis rackets) = 108
Percentage of soccer balls = (64 / 108) * 100 ≈ 59.26%
Since 59.26% is within our defined range of 53% to 63%, Week 3 is consistent with the model.
5. Total Analysis
For the Total of all 3 weeks:
Total soccer balls = 85 + 110 + 64 = 259
Total baseball bats = 30 + 22 + 21 = 73
Total tennis rackets = 31 + 23 + 23 = 77
Grand total = 259 + 73 + 77 = 409
Percentage of soccer balls = (259 / 409) * 100 ≈ 63.33%
Since 63.33% is outside our defined range of 53% to 63%, the total of all 3 weeks is inconsistent with the model.
6. Final Classification
Based on our analysis:
- Week 1: Consistent
- Week 2: Inconsistent
- Week 3: Consistent
- Total of all 3 weeks: Inconsistent
### Examples
Understanding customer preferences helps businesses optimize their inventory. For example, if a store consistently sells more soccer balls than predicted, they might increase their soccer ball stock and reduce baseball bats and tennis rackets. This ensures they meet customer demand and avoid overstocking less popular items, maximizing profits.
- Week 2's soccer ball purchase percentage is inconsistent with the model.
- Week 3's soccer ball purchase percentage is consistent with the model.
- The total soccer ball purchase percentage across all weeks is inconsistent with the model.
$\boxed{{\begin{tabular}{|c|c|}
\hline Consistent with Model & Inconsistent with Model \\
\hline Week 1 results, Week 3 results & Week 2 results, Total of all 3 weeks' results \\
\hline
\end{tabular}}}$
### Explanation
1. Analyze the problem and data
First, we need to calculate the percentage of customers who bought soccer balls for each week and for the total of all three weeks. The model predicts that 58% of customers buy soccer balls. We will classify each result as consistent or inconsistent based on how close the calculated percentage is to 58%. Let's define 'close to' as within 5 percentage points (i.e., between 53% and 63%).
2. Week 1 Analysis
For Week 1:
Total purchases = 85 (soccer balls) + 30 (baseball bats) + 31 (tennis rackets) = 146
Percentage of soccer balls = (85 / 146) * 100 ≈ 58.22%
Since 58.22% is within our defined range of 53% to 63%, Week 1 is consistent with the model.
3. Week 2 Analysis
For Week 2:
Total purchases = 110 (soccer balls) + 22 (baseball bats) + 23 (tennis rackets) = 155
Percentage of soccer balls = (110 / 155) * 100 ≈ 70.97%
Since 70.97% is outside our defined range of 53% to 63%, Week 2 is inconsistent with the model.
4. Week 3 Analysis
For Week 3:
Total purchases = 64 (soccer balls) + 21 (baseball bats) + 23 (tennis rackets) = 108
Percentage of soccer balls = (64 / 108) * 100 ≈ 59.26%
Since 59.26% is within our defined range of 53% to 63%, Week 3 is consistent with the model.
5. Total Analysis
For the Total of all 3 weeks:
Total soccer balls = 85 + 110 + 64 = 259
Total baseball bats = 30 + 22 + 21 = 73
Total tennis rackets = 31 + 23 + 23 = 77
Grand total = 259 + 73 + 77 = 409
Percentage of soccer balls = (259 / 409) * 100 ≈ 63.33%
Since 63.33% is outside our defined range of 53% to 63%, the total of all 3 weeks is inconsistent with the model.
6. Final Classification
Based on our analysis:
- Week 1: Consistent
- Week 2: Inconsistent
- Week 3: Consistent
- Total of all 3 weeks: Inconsistent
### Examples
Understanding customer preferences helps businesses optimize their inventory. For example, if a store consistently sells more soccer balls than predicted, they might increase their soccer ball stock and reduce baseball bats and tennis rackets. This ensures they meet customer demand and avoid overstocking less popular items, maximizing profits.
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