Outcomes. 2. 4. 6. 8. 10. 12

Frequency 10 9. 6. 15 13. 8

What is the smallest discrepancy between the experiment and the expected probability of this experiment? Write answer in a 3 decimal places, rounded to the nearest thousandth.

1 answer

To find the expected probability for each outcome, we divide the total frequency (which is the sum of all frequencies) by 6 (since there are 6 possible outcomes):

Expected probability of getting 2: (10+9+6+15+13+8)/6 = 4.1666667
Expected probability of getting 4: (10+9+6+15+13+8)/6 = 4.1666667
Expected probability of getting 6: (10+9+6+15+13+8)/6 = 4.1666667
Expected probability of getting 8: (10+9+6+15+13+8)/6 = 4.1666667
Expected probability of getting 10: (10+9+6+15+13+8)/6 = 4.1666667
Expected probability of getting 12: (10+9+6+15+13+8)/6 = 4.1666667

To find the discrepancy, we subtract the expected probability from the actual frequency for each outcome, take the absolute value, and add them up:

Discrepancy for outcome 2: |10 - 4.1666667| = 5.8333333
Discrepancy for outcome 4: |9 - 4.1666667| = 4.8333333
Discrepancy for outcome 6: |6 - 4.1666667| = 1.8333333
Discrepancy for outcome 8: |15 - 4.1666667| = 10.8333333
Discrepancy for outcome 10: |13 - 4.1666667| = 8.8333333
Discrepancy for outcome 12: |8 - 4.1666667| = 3.8333333

The smallest discrepancy is 1.8333333, which corresponds to outcome 6. Rounding to the nearest thousandth gives us an answer of 1.833.