Outcomes 2 4 6 8 10 12
Frequency 10 9 6 15 13]
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 probabilities, we need to calculate the expected probability first.
The total number of outcomes when rolling a standard six-sided die is 6. Since Jede's cube has faces numbered 2, 4, 6, 8, 10, and 12, the total number of outcomes on her cube is 6.
The expected probability for each outcome is 1/6 or approximately 0.1667.
Now, we can calculate the expected frequencies for each outcome:
2: 0.1667 * 63 = 10
4: 0.1667 * 63 = 10
6: 0.1667 * 63 = 10
8: 0.1667 * 63 = 10
10: 0.1667 * 63 = 10
12: 0.1667 * 63 = 10
Now, we compare the expected frequencies with the given frequencies:
Outcome 2:
Expected frequency = 10
Experimental frequency = 10
Absolute discrepancy = |10 - 10| = 0
Outcome 4:
Expected frequency = 9
Experimental frequency = 9
Absolute discrepancy = |9 - 9| = 0
Outcome 6:
Expected frequency = 6
Experimental frequency = 15
Absolute discrepancy = |6 - 15| = 9
Outcome 8:
Expected frequency = 15
Experimental frequency = 13
Absolute discrepancy = |15 - 13| = 2
Outcome 10:
Expected frequency = 13
Experimental frequency = 0
Absolute discrepancy = |13 - 0| = 13
Outcome 12:
Expected frequency = 13
Experimental frequency = 0
Absolute discrepancy = |13 - 0| = 13
The largest discrepancy is 13, which occurs for both outcomes 10 and 12.
To find the discrepancy in percentage form, we use the formula:
Discrepancy (%) = (Absolute discrepancy / Expected frequency) * 100
For outcome 10:
Discrepancy (%) = (13 / 13) * 100 = 100%
For outcome 12:
Discrepancy (%) = (13 / 13) * 100 = 100%
Therefore, the largest discrepancy between the experimental and expected probabilities of this experiment is 100%.