Let's analyze the given table to understand what the 0.3 represents. The table summarizing whether the customers ordered an appetizer and/or dessert is structured as follows:
\begin{tabular}{|c|c|c|c|}
\hline & Appetizer & No appetizer & Total \\
\hline Dessert & 0.1 & 0.3 & 0.4 \\
\hline No dessert & 0.2 & 0.4 & 0.6 \\
\hline Total & 0.3 & 0.7 & 1.0 \\
\hline
\end{tabular}
Let's break down the pertinent parts:
- The columns are "Appetizer", "No appetizer", and "Total".
- The rows are "Dessert", "No dessert", and "Total".
The highlighted cell is in the "No appetizer" column and the "Dessert" row.
To understand what the 0.3 in the highlighted cell denotes, follow these steps:
1. Column Analysis: The 0.3 lies in the "No appetizer" column. This column represents the proportion of customers who did not order an appetizer.
2. Row Analysis: The 0.3 lies in the "Total" row. This row represents the sum total of all the customers, giving relative frequencies overall.
Therefore, the 0.3 highlighted cell tells us the proportion of all customers who did not order an appetizer.
Now let's match this with the options provided:
A. [tex]$30\%$[/tex] of her customers did not order an appetizer.
- This option states that 30% of the total customers did not order an appetizer. This correctly describes the highlighted 0.3 value in the table.
B. [tex]$30\%$[/tex] of her customers ordered dessert but no appetizer.
- This option is not correct as it combines two specific categories: customers who ordered dessert AND customers who did not order an appetizer. The value 0.3 we are analyzing represents only the proportion who did not order an appetizer, regardless of their dessert order.
C. [tex]$30\%$[/tex] of her customers ordered dessert.
- This option does not match our highlighted value because it specifies the dessert order. According to the data, the total percentage of customers who ordered dessert is 0.4, not 0.3.
D. [tex]$30\%$[/tex] of the customers who ordered dessert did not order an appetizer.
- This option incorrectly constrains the analysis to customers who ordered dessert. Our focus is on the overall proportion who did not order an appetizer.
Thus, the correct interpretation of the 0.3 in the highlighted cell is:
A. [tex]$30\%$[/tex] of her customers did not order an appetizer.
