Let's carefully analyze the data given in the relative frequency table to understand what the number 0.2 represents.
First, we note that the table appears to track the relationships between ordering appetizers and desserts among the waitress's customers.
### Understanding the Table
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & \text{Appetizer} & \text{No Appetizer} & \text{Total} \\
\hline \text{Dessert} & 0.1 & 0.3 & 0.4 \\
\hline \text{No Dessert} & \textbf{0.2} & 0.4 & 0.6 \\
\hline \text{Total} & 0.3 & 0.7 & 1.0 \\
\hline
\end{tabular}
\][/tex]
### Interpreting the Highlighted Cell (0.2)
The highlighted cell, 0.2, is located at the intersection of the "No Dessert" row and the "Appetizer" column. This means it represents the relative frequency of customers who ordered an appetizer but did not order dessert.
Given this table, we can understand the implications by looking at the total customers and the relative frequencies provided for each category.
Now, let's ensure this fits contextually with the provided options:
- Option A: This option states that 20% of her customers ordered an appetizer but no dessert. This aligns perfectly with the interpretation of our highlighted cell.
- Option B: This option indicates that 20% of her customers did not order dessert, but our highlighted cell specifically refers to customers who did order an appetizer.
- Option C: This states that 20% of the customers who ordered an appetizer did not order dessert, but the table doesn't precisely correlate this with the part-to-whole ratio within the specific appetizer group alone.
- Option D: This suggests that 20% of her customers ordered an appetizer, which is represented by the total frequency of the "Appetizer" column, which is higher than 0.2.
### Conclusion
Based on the interpretation above, the correct answer is:
A. [tex]$20\%$[/tex] of her customers ordered an appetizer but no dessert.
