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A snack bar offers chili and/or cheese on its hot dogs for an additional fee. The owner kept track of the hot dog orders over the course of a week. His data are shown in a relative frequency table.

\begin{tabular}{|c|c|c|c|}
\hline
& Cheese & No cheese & Total \\
\hline
Chili & 0.1 & 0.3 & 0.4 \\
\hline
No chili & 0.2 & 0.4 & 0.6 \\
\hline
Total & 0.3 & 0.7 & 1.0 \\
\hline
\end{tabular}

What does the 0.3 in the highlighted cell mean?

A. [tex]$30 \%$[/tex] of his customers ordered chili on their hot dog.
B. [tex]$30 \%$[/tex] of his customers ordered chili but no cheese on their hot dog.
C. [tex]$30 \%$[/tex] of the customers that ordered chili ordered no cheese.
D. [tex]$30 \%$[/tex] of his customers ordered no cheese on their hot dog.

Sagot :

GinnyAnswer
To understand the meaning of the values in the relative frequency table, let's interpret the given data step-by-step.

First, let's recall what each cell in a relative frequency table represents:

- Each cell in the table presents the proportion of the total observed entries that correspond to the specific combination of categories.

Now, let's examine the table closely:

| | Cheese | No cheese | Total |
|------------------|--------|-----------|-------|
| Chili | 0.1 | 0.3 | 0.4 |
| No chili | 0.2 | 0.4 | 0.6 |
| Total | 0.3 | 0.7 | 1.0 |

The highlighted cell is in the row labeled "Chili" and the column labeled "No cheese". Therefore, it represents the proportion of customers that ordered chili but no cheese on their hot dog.

To verify our understanding:
- Looking at the row for "Chili":
- 0.1 means the proportion of customers ordered chili with cheese.
- 0.3 means the proportion of customers ordered chili but no cheese.
- 0.4 is the total proportion for customers who ordered chili in any form.

Thus, the 0.3 specifically indicates the proportion of customers who ordered chili but no cheese on their hot dog, which translates to [tex]\(0.3 \times 100 = 30\%\)[/tex].

Therefore, the correct interpretation of the 0.3 in the highlighted cell is:

B. [tex]\(30\%\)[/tex] of his customers ordered chili but no cheese on their hot dog.
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