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Answer :
- Calculate the percentage of soccer ball purchases for each week and the total.
- Week 1: $\frac{85}{146} \approx 58\%$ (Consistent)
- Week 2: $\frac{110}{155} \approx 71\%$ (Inconsistent)
- Week 3: $\frac{64}{108} \approx 59\%$ (Consistent)
- Total: $\frac{259}{409} \approx 63\%$ (Consistent)
- Classify each result based on whether it falls within the $53\%$ to $63\%$ range.
$\boxed{{\text{Week 1: Consistent, Week 2: Inconsistent, Week 3: Consistent, Total: Consistent}}}$
### Explanation
1. Analyze the problem and data
The model predicts that $58\%$ of customers purchase soccer balls. We will calculate the percentage of soccer ball purchases for each week and overall, then compare these percentages to the model's prediction. We'll consider a result 'consistent' if it falls within $53\%$ to $63\%$.
2. Calculate Week 1 percentage
For Week 1:
Total customers = $85 + 30 + 31 = 146$
Percentage of soccer ball purchases = $\frac{85}{146} \approx 0.58 = 58\%$
This is consistent with the model (within $53\%$ to $63\%$).
3. Calculate Week 2 percentage
For Week 2:
Total customers = $110 + 22 + 23 = 155$
Percentage of soccer ball purchases = $\frac{110}{155} \approx 0.71 = 71\%$
This is inconsistent with the model (outside $53\%$ to $63\%$).
4. Calculate Week 3 percentage
For Week 3:
Total customers = $64 + 21 + 23 = 108$
Percentage of soccer ball purchases = $\frac{64}{108} \approx 0.59 = 59\%$
This is consistent with the model (within $53\%$ to $63\%$).
5. Calculate overall percentage
For the Total of all 3 weeks:
Total customers = $146 + 155 + 108 = 409$
Total soccer balls = $85 + 110 + 64 = 259$
Percentage of soccer ball purchases = $\frac{259}{409} \approx 0.63 = 63\%$
This is consistent with the model (within $53\%$ to $63\%$).
6. Final Classification
Based on our calculations:
- Week 1: Consistent
- Week 2: Inconsistent
- Week 3: Consistent
- Total: Consistent
### Examples
Understanding customer preferences helps businesses optimize their inventory. For example, if a store consistently sells more soccer balls than expected, they can increase their soccer ball stock and reduce baseball bats and tennis rackets to meet demand and maximize profits.
- Week 1: $\frac{85}{146} \approx 58\%$ (Consistent)
- Week 2: $\frac{110}{155} \approx 71\%$ (Inconsistent)
- Week 3: $\frac{64}{108} \approx 59\%$ (Consistent)
- Total: $\frac{259}{409} \approx 63\%$ (Consistent)
- Classify each result based on whether it falls within the $53\%$ to $63\%$ range.
$\boxed{{\text{Week 1: Consistent, Week 2: Inconsistent, Week 3: Consistent, Total: Consistent}}}$
### Explanation
1. Analyze the problem and data
The model predicts that $58\%$ of customers purchase soccer balls. We will calculate the percentage of soccer ball purchases for each week and overall, then compare these percentages to the model's prediction. We'll consider a result 'consistent' if it falls within $53\%$ to $63\%$.
2. Calculate Week 1 percentage
For Week 1:
Total customers = $85 + 30 + 31 = 146$
Percentage of soccer ball purchases = $\frac{85}{146} \approx 0.58 = 58\%$
This is consistent with the model (within $53\%$ to $63\%$).
3. Calculate Week 2 percentage
For Week 2:
Total customers = $110 + 22 + 23 = 155$
Percentage of soccer ball purchases = $\frac{110}{155} \approx 0.71 = 71\%$
This is inconsistent with the model (outside $53\%$ to $63\%$).
4. Calculate Week 3 percentage
For Week 3:
Total customers = $64 + 21 + 23 = 108$
Percentage of soccer ball purchases = $\frac{64}{108} \approx 0.59 = 59\%$
This is consistent with the model (within $53\%$ to $63\%$).
5. Calculate overall percentage
For the Total of all 3 weeks:
Total customers = $146 + 155 + 108 = 409$
Total soccer balls = $85 + 110 + 64 = 259$
Percentage of soccer ball purchases = $\frac{259}{409} \approx 0.63 = 63\%$
This is consistent with the model (within $53\%$ to $63\%$).
6. Final Classification
Based on our calculations:
- Week 1: Consistent
- Week 2: Inconsistent
- Week 3: Consistent
- Total: Consistent
### Examples
Understanding customer preferences helps businesses optimize their inventory. For example, if a store consistently sells more soccer balls than expected, they can increase their soccer ball stock and reduce baseball bats and tennis rackets to meet demand and maximize profits.
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