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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 find the percentage of students who prefer sprinkles or jelly beans for each ice cream flavor (Vanilla and Chocolate), given that they prefer Chocolate or Vanilla.

First, we'll calculate the percentages for Vanilla:

Vanilla:

  • Students preferring sprinkles: 102
  • Total students preferring Vanilla: 175

To find the percentage of Vanilla voters who prefer sprinkles: \[ \text{Percentage of Sprinkles for Vanilla} = \left(\frac{102}{175}\right) \times 100 \approx 58.29 % \] Rounding to the nearest whole percentage gives approximately 58%.

Now for Jelly Beans:

  • Students preferring jelly beans: 73
  • Total students preferring Vanilla: 175

To find the percentage of Vanilla voters who prefer jelly beans: \[ \text{Percentage of Jelly Beans for Vanilla} = \left(\frac{73}{175}\right) \times 100 \approx 41.71 % \] Rounding to the nearest whole percentage gives approximately 42%.

Now, we summarize the results:

  • For Vanilla:
    • Sprinkles: 58%
    • Jelly Beans: 42%

Now for Chocolate:

Chocolate:

  • Students preferring sprinkles: 65
  • Total students preferring Chocolate: 190

To find the percentage of Chocolate voters who prefer sprinkles: \[ \text{Percentage of Sprinkles for Chocolate} = \left(\frac{65}{190}\right) \times 100 \approx 34.21 % \] Rounding to the nearest whole percentage gives approximately 34%.

Now for Jelly Beans:

  • Students preferring jelly beans: 125
  • Total students preferring Chocolate: 190

To find the percentage of Chocolate voters who prefer jelly beans: \[ \text{Percentage of Jelly Beans for Chocolate} = \left(\frac{125}{190}\right) \times 100 \approx 65.79 % \] Rounding to the nearest whole percentage gives approximately 66%.

So the complete table of conditional relative frequencies is as follows:

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

Here's the final two-way table with the filled-in values:

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