Use the table to answer the question.
Outcomes 2 4 6 8 10 12
Frequency 10 9 6 15 13 8
Jede tossed a cube with faces numbered with 2, 4, 6, 8, 10, and 12. The results are recorded in the table. What is the largest discrepancy between the experimental and the expected probability of this experiment? The answer needs to be in percent form to the nearest whole number.
(1 point)
%
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To find the largest discrepancy between the experimental and expected probability, we first need to calculate the expected probability for each outcome. Since Jede tossed a cube with 6 faces numbered 2, 4, 6, 8, 10, and 12, the probability of each outcome is 1/6 or approximately 16.67%.
Now, let's calculate the actual percentage frequency of each outcome:
- For outcome 2: 10/61 ≈ 0.164 or 16.4%
- For outcome 4: 9/61 ≈ 0.148 or 14.8%
- For outcome 6: 6/61 ≈ 0.098 or 9.8%
- For outcome 8: 15/61 ≈ 0.246 or 24.6%
- For outcome 10: 13/61 ≈ 0.213 or 21.3%
- For outcome 12: 8/61 ≈ 0.131 or 13.1%
Now, we calculate the discrepancies for each outcome:
- For outcome 2: |16.4 - 16.67| ≈ 0.27%
- For outcome 4: |14.8 - 16.67| ≈ 1.87%
- For outcome 6: |9.8 - 16.67| ≈ 6.87%
- For outcome 8: |24.6 - 16.67| ≈ 7.93%
- For outcome 10: |21.3 - 16.67| ≈ 4.63%
- For outcome 12: |13.1 - 16.67| ≈ 3.57%
The largest discrepancy is for outcome 8, with a percentage discrepancy of approximately 7.93%.