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.
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To find the expected probability of each outcome, we divide each frequency by the total number of trials:
Outcomes 2 4 6 8 10 12 Total
Frequency 10 9 6 15 13 8 61
Expected Probability 10/61 9/61 6/61 15/61 13/61 8/61
To find the experimental probability, we need to add up all the frequencies and divide each frequency by the total:
Experimental Probability 10/61 9/61 6/61 15/61 13/61 8/61
To find the discrepancy between the experimental probability and the expected probability, we subtract the expected probability from the experimental probability and take the absolute value:
|Experimental Probability - Expected Probability|
|10/61 - 1/6| |9/61 - 1/6| |6/61 - 1/6| |15/61 - 1/6| |13/61 - 1/6| |8/61 - 1/6|
|0.027 |0.024| 0.023| 0.002| 0.008| 0.023|
The largest discrepancy is 0.027, which corresponds to the outcome of 2. Converting to a percentage and rounding to the nearest whole number, the largest discrepancy is 3%.