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Drag each label to the correct location on the table.

The manager of Gerard's Restaurant is making a supply order for the coming week. Based on his past experience, the manager has constructed a model which shows that pasta is chosen over salad and enchiladas [tex]$62 \%$[/tex] of the time.

The table below shows the results of three days of business, with breakdowns for how many customers ordered pasta, salad, and enchiladas.

\begin{tabular}{|c|c|c|c|}
\hline Day & Pasta & Salad & Enchiladas \\
\hline 1 & 130 & 37 & 38 \\
\hline 2 & 175 & 17 & 14 \\
\hline 3 & 105 & 31 & 33 \\
\hline
\end{tabular}

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

\begin{tabular}{|c|c|}
\hline
\begin{tabular}{c}
Consistent with \\
Model
\end{tabular} & \begin{tabular}{c}
Inconsistent with \\
Model
\end{tabular} \\
\hline
& \\
& \\
\hline
\end{tabular}

Sagot :

GinnyAnsweridn
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]
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