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The owner of a sporting goods store is making a supply purchase for the coming month. Based on past experience, he has constructed a model which shows that customers choose to buy soccer balls over baseball bats and tennis rackets [tex]58\%[/tex] of the time.

The table below shows the results of three weeks of business with breakdowns for how many customers purchased soccer balls, baseball bats, and tennis rackets.

\begin{tabular}{|c|c|c|c|}
\hline Week & Soccer Balls & Baseball Bats & Tennis Rackets \\
\hline 1 & 85 & 30 & 31 \\
\hline 2 & 110 & 22 & 23 \\
\hline 3 & 64 & 21 & 23 \\
\hline
\end{tabular}

Classify the results for each category as either consistent or inconsistent with the model.

\begin{tabular}{|l|c|}
\hline \begin{tabular}{c}
Category
\end{tabular} & \begin{tabular}{c}
Consistency
\end{tabular} \\
\hline Week 1 results & \\
\hline Week 2 results & \\
\hline Week 3 results & \\
\hline Total of all 3 weeks' results & \\
\hline
\end{tabular}

Sagot :

GinnyAnsweridn
To classify the results for each category as either consistent or inconsistent with the model, let's break down the numbers step by step for each week and the total of all three weeks. The model predicts that 58% of the time customers will purchase soccer balls. We'll compare the actual percentages with the expected percentage to determine consistency.

### Week 1
- Soccer Balls: 85
- Baseball Bats: 30
- Tennis Rackets: 31
- Total Customers: 85 (soccer balls) + 30 (baseball bats) + 31 (tennis rackets) = 146

Percentage of Soccer Ball Purchases:
[tex]\[ \frac{85}{146} \approx 0.582 \text{ or } 58.2\% \][/tex]
Since [tex]\( 58.2\% \approx 58\% \)[/tex], this week's result is consistent with the model.

### Week 2
- Soccer Balls: 110
- Baseball Bats: 22
- Tennis Rackets: 23
- Total Customers: 110 (soccer balls) + 22 (baseball bats) + 23 (tennis rackets) = 155

Percentage of Soccer Ball Purchases:
[tex]\[ \frac{110}{155} \approx 0.710 \text{ or } 71.0\% \][/tex]
Since [tex]\( 71.0\% \)[/tex] is considerably higher than [tex]\( 58\% \)[/tex] by more than 4 or 5 percentage points, this week's result is inconsistent with the model.

### Week 3
- Soccer Balls: 64
- Baseball Bats: 21
- Tennis Rackets: 23
- Total Customers: 64 (soccer balls) + 21 (baseball bats) + 23 (tennis rackets) = 108

Percentage of Soccer Ball Purchases:
[tex]\[ \frac{64}{108} \approx 0.593 \text{ or } 59.3\% \][/tex]
Since [tex]\( 59.3\% \approx 58\% \)[/tex], this week's result is consistent with the model.

### 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
- Total Customers: 259 (soccer balls) + 73 (baseball bats) + 77 (tennis rackets) = 409

Overall Percentage of Soccer Ball Purchases:
[tex]\[ \frac{259}{409} \approx 0.633 \text{ or } 63.3\% \][/tex]
Since [tex]\( 63.3\% \)[/tex] is higher than [tex]\( 58\% \)[/tex] by more than 4 or 5 percentage points, the overall result is inconsistent with the model.

### Summary
\begin{tabular}{|l|c|}
\hline \begin{tabular}{c}
Consistent with \\
Model
\end{tabular} & \begin{tabular}{c}
Inconsistent with \\
Model
\end{tabular} \\
\hline
- Week 1 & - Week 2 \\
- Week 3 & - Total of all 3 weeks \\
\hline
\end{tabular}
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