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Use the table to answer the 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.

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

1 answer

To generate a two-way table of conditional relative frequencies, we need to calculate the percentage of students preferring sprinkles or jelly beans within each flavor category (Vanilla and Chocolate). We will take the total votes for each flavor (Vanilla or Chocolate) as the denominator for our calculations.

From the table:

  • Total votes for Vanilla: 175
  • Total votes for Chocolate: 190

For Vanilla:

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

To find the percentages:

  • Percentage for Sprinkles (Vanilla) = (Votes for Sprinkles / Total Vanilla Votes) * 100 = (102 / 175) * 100 ≈ 58.3% (rounded to 58%)

  • Percentage for Jelly Beans (Vanilla) = (Votes for Jelly Beans / Total Vanilla Votes) * 100 = (73 / 175) * 100 ≈ 41.7% (rounded to 42%)

For Chocolate:

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

To find the percentages:

  • Percentage for Sprinkles (Chocolate) = (Votes for Sprinkles / Total Chocolate Votes) * 100 = (65 / 190) * 100 ≈ 34.2% (rounded to 34%)

  • Percentage for Jelly Beans (Chocolate) = (Votes for Jelly Beans / Total Chocolate Votes) * 100 = (125 / 190) * 100 ≈ 65.8% (rounded to 66%)

Summary of the Conditional Relative Frequencies:

\[ \begin{array}{|c|c|c|} \hline & \text{Sprinkles (%)} & \text{Jelly Beans (%)} \ \hline \text{Vanilla} & 58 & 42 \ \hline \text{Chocolate} & 34 & 66 \ \hline \end{array} \]

So the final table is:

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