Answer :
Let's determine whether the results for each day are consistent or inconsistent with the model.
### Step-by-Step Solution
1. Day 1:
- Pasta: 130
- Salad: 37
- Enchiladas: 38
- Total customers: [tex]\(130 + 37 + 38 = 205\)[/tex]
- Percentage choosing pasta: [tex]\(\frac{130}{205} \approx 0.634\)[/tex] or [tex]\(63.4\%\)[/tex]
2. Day 2:
- Pasta: 175
- Salad: 17
- Enchiladas: 14
- Total customers: [tex]\(175 + 17 + 14 = 206\)[/tex]
- Percentage choosing pasta: [tex]\(\frac{175}{206} \approx 0.850\)[/tex] or [tex]\(85.0\%\)[/tex]
3. Day 3:
- Pasta: 105
- Salad: 31
- Enchiladas: 33
- Total customers: [tex]\(105 + 31 + 33 = 169\)[/tex]
- Percentage choosing pasta: [tex]\(\frac{105}{169} \approx 0.621\)[/tex] or [tex]\(62.1\%\)[/tex]
### Comparing to the model:
- The model predicts that pasta would be chosen [tex]\(62\%\)[/tex] of the time, and we consider it consistent if it falls within [tex]\( \pm 5 \% \)[/tex] of this percentage ([tex]\(57\%\)[/tex] to [tex]\(67\%\)[/tex]).
- For Day 1: [tex]\(63.4\%\)[/tex] (which is within [tex]\(62\% \pm 5\%\)[/tex])
- For Day 2: [tex]\(85.0\%\)[/tex] (which is outside [tex]\(62\% \pm 5\%\)[/tex])
- For Day 3: [tex]\(62.1\%\)[/tex] (which is within [tex]\(62\% \pm 5\%\)[/tex])
So, the results of Day 1 and Day 3 are consistent with the model, and the results of Day 2 are inconsistent with the model.
### Conclusion
Classify the days into the correct categories:
[tex]\[ \begin{tabular}{|c|c|} \hline \text{Consistent with Model} & \text{Inconsistent with Model} \\ \hline 1, 3 & 2 \\ \hline \end{tabular} \][/tex]
### Step-by-Step Solution
1. Day 1:
- Pasta: 130
- Salad: 37
- Enchiladas: 38
- Total customers: [tex]\(130 + 37 + 38 = 205\)[/tex]
- Percentage choosing pasta: [tex]\(\frac{130}{205} \approx 0.634\)[/tex] or [tex]\(63.4\%\)[/tex]
2. Day 2:
- Pasta: 175
- Salad: 17
- Enchiladas: 14
- Total customers: [tex]\(175 + 17 + 14 = 206\)[/tex]
- Percentage choosing pasta: [tex]\(\frac{175}{206} \approx 0.850\)[/tex] or [tex]\(85.0\%\)[/tex]
3. Day 3:
- Pasta: 105
- Salad: 31
- Enchiladas: 33
- Total customers: [tex]\(105 + 31 + 33 = 169\)[/tex]
- Percentage choosing pasta: [tex]\(\frac{105}{169} \approx 0.621\)[/tex] or [tex]\(62.1\%\)[/tex]
### Comparing to the model:
- The model predicts that pasta would be chosen [tex]\(62\%\)[/tex] of the time, and we consider it consistent if it falls within [tex]\( \pm 5 \% \)[/tex] of this percentage ([tex]\(57\%\)[/tex] to [tex]\(67\%\)[/tex]).
- For Day 1: [tex]\(63.4\%\)[/tex] (which is within [tex]\(62\% \pm 5\%\)[/tex])
- For Day 2: [tex]\(85.0\%\)[/tex] (which is outside [tex]\(62\% \pm 5\%\)[/tex])
- For Day 3: [tex]\(62.1\%\)[/tex] (which is within [tex]\(62\% \pm 5\%\)[/tex])
So, the results of Day 1 and Day 3 are consistent with the model, and the results of Day 2 are inconsistent with the model.
### Conclusion
Classify the days into the correct categories:
[tex]\[ \begin{tabular}{|c|c|} \hline \text{Consistent with Model} & \text{Inconsistent with Model} \\ \hline 1, 3 & 2 \\ \hline \end{tabular} \][/tex]