A)
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? Write your answer in 3 decimal places, rounded to the nearest thousandth.
To find the expected probability for each outcome, we need to divide the total frequency (61) by the total number of outcomes (6).
Expected probability = Total frequency / Total number of outcomes = 61 / 6 ≈ 10.167
Now, we can calculate the discrepancies for each outcome by subtracting the expected probability from the experimental probability and taking the absolute value. Then, we find the smallest discrepancy.
|2: Discrepancy = |10/61 - 10.167| = 0.167
|4: Discrepancy = |9/61 - 10.167| = 1.167
|6: Discrepancy = |6/61 - 10.167| = 4.167
|8: Discrepancy = |15/61 - 10.167| = 4.833
|10: Discrepancy = |13/61 - 10.167| = 2.833
|12: Discrepancy = |8/61 - 10.167| = 2.167
The smallest discrepancy is 0.167, so the answer is 0.167.