Use the table to answer the question.

Question

Sprinkles Jelly Beans Total
Vanilla 102 73 175
Chocolate 65 125 190
Total 167 198 365
You have gathered your grade’s votes for favorite ice cream flavor and topping. Then you organized the data into a two-way frequency table. Interpret the table to generate a two-way table of conditional relative frequencies for students who prefer sprinkles or jelly beans, given they prefer chocolate or vanilla. Round your answers to the nearest whole percentage.

Sprinkles (%) Jelly Beans (%)
Vanilla % %
Chocolate 34 66

Answer 1

To find the conditional relative frequencies, we first need to calculate the total votes for each ice cream flavor (vanilla and chocolate). We can then determine the percentages of students who prefer sprinkles and jelly beans for each flavor.

The total votes for each flavor:

• Total for Vanilla = 175
• Total for Chocolate = 190

Now, let's calculate the conditional relative frequencies:

1. For Vanilla:

   • Votes for Sprinkles: 102
   • Votes for Jelly Beans: 73

   Conditional relative frequencies for Vanilla:

   • Sprinkles: \( \frac{102}{175} \times 100 \approx 58.29% \) (rounded to 58%)
   • Jelly Beans: \( \frac{73}{175} \times 100 \approx 41.71% \) (rounded to 42%)

2. For Chocolate:

   • Votes for Sprinkles: 65
   • Votes for Jelly Beans: 125

   Conditional relative frequencies for Chocolate:

   • Sprinkles: \( \frac{65}{190} \times 100 \approx 34.21% \) (rounded to 34%)
   • Jelly Beans: \( \frac{125}{190} \times 100 \approx 65.79% \) (rounded to 66%)

Now we can fill in the two-way conditional relative frequency table:

| | Sprinkles (%) | Jelly Beans (%) | |-------------|----------------|-----------------| | Vanilla | 58% | 42% | | Chocolate | 34% | 66% |

Thus, the final answers are:

• For Vanilla: Sprinkles = 58%, Jelly Beans = 42%
• For Chocolate: Sprinkles = 34%, Jelly Beans = 66%