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.
To find the largest discrepancy between the experimental and expected probability, we first need to calculate the expected probability for each outcome.
The total number of outcomes is 10 + 9 + 6 + 15 + 13 + 8 = 61.
The expected probability for each outcome is calculated as:
- P(2) = 1/6
- P(4) = 1/6
- P(6) = 1/6
- P(8) = 1/6
- P(10) = 1/6
- P(12) = 1/6
Now, we calculate the expected frequency for each outcome:
- E(2) = 1/6 * 61 = 10.17
- E(4) = 1/6 * 61 = 10.17
- E(6) = 1/6 * 61 = 10.17
- E(8) = 1/6 * 61 = 10.17
- E(10) = 1/6 * 61 = 10.17
- E(12) = 1/6 * 61 = 10.17
Next, we calculate the discrepancy for each outcome:
- |10 - 10.17| = 0.17
- |9 - 10.17| = 1.17
- |6 - 10.17| = 4.17
- |15 - 10.17| = 4.83
- |13 - 10.17| = 2.83
- |8 - 10.17| = 2.17
The largest discrepancy is 4.83.
To find the largest discrepancy in percentage form, we calculate: (4.83 / 61) * 100% = 7.91%
Therefore, the largest discrepancy between the experimental and expected probability in this experiment is 8% to the nearest whole number.
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? Write your answer in 3 decimal places, rounded to the nearest thousandth
To find the smallest discrepancy between the experimental and expected probability, we follow a similar process as in the previous question.
First, we calculate the total number of outcomes, which is 10 + 9 + 6 + 15 + 13 + 8 = 61.
The expected probability for each outcome is:
- P(2) = 1/6
- P(4) = 1/6
- P(6) = 1/6
- P(8) = 1/6
- P(10) = 1/6
- P(12) = 1/6
The expected frequency for each outcome is:
- E(2) = 1/6 * 61 = 10.17
- E(4) = 1/6 * 61 = 10.17
- E(6) = 1/6 * 61 = 10.17
- E(8) = 1/6 * 61 = 10.17
- E(10) = 1/6 * 61 = 10.17
- E(12) = 1/6 * 61 = 10.17
Next, we calculate the discrepancy for each outcome:
- |10 - 10.17| = 0.17
- |9 - 10.17| = 1.17
- |6 - 10.17| = 4.17
- |15 - 10.17| = 4.83
- |13 - 10.17| = 2.83
- |8 - 10.17| = 2.17
The smallest discrepancy is 0.17.
Rounded to three decimal places, the smallest discrepancy is 0.170.
wrong
Apologies for the error. Let's recalculate the smallest discrepancy between the experimental and expected probabilities:
The smallest discrepancy occurs when we calculate the discrepancy for the outcome with the smallest difference between the experimental and expected frequencies.
For outcome 2 (Frequency = 10):
- Expected frequency (E) = (1/6) * 61 ≈ 10.167
- Discrepancy = |10 - 10.167| ≈ 0.167
For outcome 8 (Frequency = 15):
- Expected frequency (E) = (1/6) * 61 ≈ 10.167
- Discrepancy = |15 - 10.167| ≈ 4.833
For outcome 12 (Frequency = 8):
- Expected frequency (E) = (1/6) * 61 ≈ 10.167
- Discrepancy = |8 - 10.167| ≈ 2.167
The smallest discrepancy between the experimental and expected probability is approximately 0.167 rounded to three decimal places.