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 smallest discrepancy between the experimental and the expected probability of this experiment? The answer needs to be in percent form to the nearest thousandth.
(0.3 is Wrong)
boi. even copilot is better than you
The expected probability of each outcome is 1/6 or approximately 0.167.
To find the discrepancy between the experimental and expected probability for each outcome, we can calculate the absolute difference between the experimental and expected probabilities, and then divide by the expected probability:
For outcome 2: |10/61 - 1/6| / 1/6 = 4/61 ≈ 0.066
For outcome 4: |9/61 - 1/6| / 1/6 = 7/122 ≈ 0.057
For outcome 6: |6/61 - 1/6| / 1/6 = 1/61 ≈ 0.016
For outcome 8: |15/61 - 1/6| / 1/6 = 25/366 ≈ 0.068
For outcome 10: |13/61 - 1/6| / 1/6 = 23/366 ≈ 0.063
For outcome 12: |8/61 - 1/6| / 1/6 = 19/366 ≈ 0.052
The smallest discrepancy is approximately 0.016 or 1.6%.
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 smallest discrepancy between the experimental and the expected probability of this experiment? The answer needs to be in percent form to the nearest thousandth.
(0.3 AND 1.6 are wrong)
To find the smallest discrepancy between the experimental and expected probability, you would first need to calculate the expected probability of each outcome, which is 1/6 = 0.167.
Then, you'd calculate the observed probability for each outcome by dividing the frequency by the total number of trials, which is ∑ frequency = 10 + 9 + 6 + 15 + 13 + 8 = 61.
Now, for each outcome:
- For outcome 2, the observed probability is 10/61 ≈ 0.164.
- For outcome 4, the observed probability is 9/61 ≈ 0.148.
- For outcome 6, the observed probability is 6/61 ≈ 0.098.
- For outcome 8, the observed probability is 15/61 ≈ 0.246.
- For outcome 10, the observed probability is 13/61 ≈ 0.213.
- For outcome 12, the observed probability is 8/61 ≈ 0.131.
Now, find the absolute difference between the experimental and observed probabilities for each outcome:
- For outcome 2: |0.167 - 0.164| = 0.003
- For outcome 4: |0.167 - 0.148| = 0.019
- For outcome 6: |0.167 - 0.098| = 0.069
- For outcome 8: |0.167 - 0.246| = 0.079
- For outcome 10: |0.167 - 0.213| = 0.046
- For outcome 12: |0.167 - 0.131| = 0.036
The smallest discrepancy is 0.003, which is equivalent to 0.3% when converted to percent form. Thus, the correct answer is 0.3%.
...
I made a mistake in my previous responses. I apologize for the confusion. Let's correct the calculation.
The expected probability for each outcome is 1/6 ≈ 0.167.
The observed probabilities for each outcome are:
- Outcome 2: 10/61 ≈ 0.164
- Outcome 4: 9/61 ≈ 0.148
- Outcome 6: 6/61 ≈ 0.098
- Outcome 8: 15/61 ≈ 0.246
- Outcome 10: 13/61 ≈ 0.213
- Outcome 12: 8/61 ≈ 0.131
The discrepancies between the experimental and expected probabilities for each outcome are:
- Outcome 2: |0.167 - 0.164| = 0.003
- Outcome 4: |0.167 - 0.148| = 0.019
- Outcome 6: |0.167 - 0.098| = 0.069
- Outcome 8: |0.167 - 0.246| = 0.079
- Outcome 10: |0.167 - 0.213| = 0.046
- Outcome 12: |0.167 - 0.131| = 0.036
The smallest discrepancy is 0.003, which is equivalent to 0.3% when converted to percent form. Therefore, the correct answer is 0.3%. Thank you for your patience.