Question

Hamburgers Hot Dogs Total
Soda 41 20 61
Water 31 28 59
Total 72 48 120
Use the two-way frequency table to complete the conditional frequency table for students who prefer soda or water given they prefer hamburgers or hot dogs. Round each percentage to the nearest whole number.

(1 point)
Hamburgers (%) Hot Dogs(%) Total(%)
Soda
%
% 100
Water 53 47 100

Answer 1

To find the conditional frequencies (percentages) for the students who prefer soda or water given they prefer hamburgers or hot dogs, we calculate the percentages based on the totals for hamburgers and hot dogs.

### Given Data
- Total for Hamburgers: 72
- Total for Hot Dogs: 48
- Overall Total: 120

### For Soda
- Students who prefer soda and hamburgers: 41
- Students who prefer soda and hot dogs: 20

Now, we can calculate the percentages:
1. For hamburgers:
\[
\text{Soda with Hamburgers} = \left( \frac{41}{72} \right) \times 100 \approx 56.94\% \approx 57\%
\]

2. For hot dogs:
\[
\text{Soda with Hot Dogs} = \left( \frac{20}{48} \right) \times 100 \approx 41.67\% \approx 42\%
\]

### For Water
- Students who prefer water and hamburgers: 31
- Students who prefer water and hot dogs: 28

Calculating the percentages for water:
1. For hamburgers:
\[
\text{Water with Hamburgers} = \left( \frac{31}{72} \right) \times 100 \approx 43.06\% \approx 43\%
\]

2. For hot dogs:
\[
\text{Water with Hot Dogs} = \left( \frac{28}{48} \right) \times 100 \approx 58.33\% \approx 58\%
\]

### Conditional Frequency Table

The completed conditional frequency table (rounded to the nearest whole number) is as follows:

| | Hamburgers (%) | Hot Dogs (%) | Total (%) |
|------------------|----------------|--------------|-----------|
| Soda | 57 | 42 | 100 |
| Water | 43 | 58 | 100 |

Thus, your conditional frequencies for soda are:
- Hamburgers: **57%**
- Hot Dogs: **42%**

The final conditional frequency table looks like this:

| | Hamburgers (%) | Hot Dogs (%) | Total (%) |
|------------------|----------------|--------------|-----------|
| Soda | 57 | 42 | 100 |
| Water | 43 | 58 | 100 |