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Answer :
- Calculate the percentage of soccer ball purchases for each week and the total.
- Week 1: $\approx 58.22\%$, Week 2: $\approx 70.97\%$, Week 3: $\approx 59.26\%$, Total: $\approx 63.33\%$.
- Compare each percentage to the model's prediction of $58\%$ and a consistency range of $53\%$ to $63\%$.
- Classify each result: Week 1 is consistent, Week 2 is inconsistent, Week 3 is consistent, and the total is inconsistent. $\boxed{}$
### Explanation
1. Calculate Percentages
First, we need to calculate the percentage of soccer ball purchases for each week and for all weeks combined. We already have the number of soccer balls, baseball bats, and tennis rackets purchased each week.
2. Week 1 Percentage
Week 1: Total purchases = $85 + 30 + 31 = 146$. Soccer ball percentage = $\frac{85}{146} \times 100 \approx 58.22\%$
3. Week 2 Percentage
Week 2: Total purchases = $110 + 22 + 23 = 155$. Soccer ball percentage = $\frac{110}{155} \times 100 \approx 70.97\%$
4. Week 3 Percentage
Week 3: Total purchases = $64 + 21 + 23 = 108$. Soccer ball percentage = $\frac{64}{108} \times 100 \approx 59.26\%$
5. Total Percentage
Total of all weeks: Total soccer balls = $85 + 110 + 64 = 259$. Total purchases = $146 + 155 + 108 = 409$. Soccer ball percentage = $\frac{259}{409} \times 100 \approx 63.33\%$
6. Compare to Model
Now, we compare each percentage to the model's prediction of $58\%$. We'll consider a range of $5\%$ around $58\%$ (i.e., $53\%$ to $63\%$) as consistent with the model.
7. Classify Results
Week 1: $58.22\%$ is within the $53\%$ to $63\%$ range, so it's consistent.
Week 2: $70.97\%$ is outside the $53\%$ to $63\%$ range, so it's inconsistent.
Week 3: $59.26\%$ is within the $53\%$ to $63\%$ range, so it's consistent.
Total: $63.33\%$ is slightly outside the $53\%$ to $63\%$ range, but let's consider a slightly wider range of $53\%$ to $64\%$ to account for the accumulation of data. Thus, it is still inconsistent.
8. 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 is crucial for businesses. For instance, a clothing store might use similar analysis to determine which styles are most popular each week and adjust their inventory accordingly. This ensures they stock what customers want, maximizing sales and minimizing losses on unpopular items.
- Week 1: $\approx 58.22\%$, Week 2: $\approx 70.97\%$, Week 3: $\approx 59.26\%$, Total: $\approx 63.33\%$.
- Compare each percentage to the model's prediction of $58\%$ and a consistency range of $53\%$ to $63\%$.
- Classify each result: Week 1 is consistent, Week 2 is inconsistent, Week 3 is consistent, and the total is inconsistent. $\boxed{}$
### Explanation
1. Calculate Percentages
First, we need to calculate the percentage of soccer ball purchases for each week and for all weeks combined. We already have the number of soccer balls, baseball bats, and tennis rackets purchased each week.
2. Week 1 Percentage
Week 1: Total purchases = $85 + 30 + 31 = 146$. Soccer ball percentage = $\frac{85}{146} \times 100 \approx 58.22\%$
3. Week 2 Percentage
Week 2: Total purchases = $110 + 22 + 23 = 155$. Soccer ball percentage = $\frac{110}{155} \times 100 \approx 70.97\%$
4. Week 3 Percentage
Week 3: Total purchases = $64 + 21 + 23 = 108$. Soccer ball percentage = $\frac{64}{108} \times 100 \approx 59.26\%$
5. Total Percentage
Total of all weeks: Total soccer balls = $85 + 110 + 64 = 259$. Total purchases = $146 + 155 + 108 = 409$. Soccer ball percentage = $\frac{259}{409} \times 100 \approx 63.33\%$
6. Compare to Model
Now, we compare each percentage to the model's prediction of $58\%$. We'll consider a range of $5\%$ around $58\%$ (i.e., $53\%$ to $63\%$) as consistent with the model.
7. Classify Results
Week 1: $58.22\%$ is within the $53\%$ to $63\%$ range, so it's consistent.
Week 2: $70.97\%$ is outside the $53\%$ to $63\%$ range, so it's inconsistent.
Week 3: $59.26\%$ is within the $53\%$ to $63\%$ range, so it's consistent.
Total: $63.33\%$ is slightly outside the $53\%$ to $63\%$ range, but let's consider a slightly wider range of $53\%$ to $64\%$ to account for the accumulation of data. Thus, it is still inconsistent.
8. 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 is crucial for businesses. For instance, a clothing store might use similar analysis to determine which styles are most popular each week and adjust their inventory accordingly. This ensures they stock what customers want, maximizing sales and minimizing losses on unpopular items.
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