Question

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. (1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The expected probability for each outcome is 1/6 or approximately 0.167.

To find the discrepancy between the experimental and expected probability, we need to calculate the absolute difference between the experimental and expected probabilities for each outcome, then find the smallest difference.

For outcome 2:
Experimental probability = 10/61 ≈ 0.164
Absolute difference = |0.164 - 0.167| ≈ 0.003

For outcome 4:
Experimental probability = 9/61 ≈ 0.148
Absolute difference = |0.148 - 0.167| ≈ 0.019

For outcome 6:
Experimental probability = 6/61 ≈ 0.098
Absolute difference = |0.098 - 0.167| ≈ 0.069

For outcome 8:
Experimental probability = 15/61 ≈ 0.246
Absolute difference = |0.246 - 0.167| ≈ 0.079

For outcome 10:
Experimental probability = 13/61 ≈ 0.213
Absolute difference = |0.213 - 0.167| ≈ 0.046

For outcome 12:
Experimental probability = 8/61 ≈ 0.131
Absolute difference = |0.131 - 0.167| ≈ 0.036

The smallest discrepancy between the experimental and expected probability is 0.003.

Answer 2

r u sure

Answer 3

[AI-generated answer — Bot GPT 3.5]

Let's recheck the calculations for the discrepancies between the experimental and expected probabilities:

For outcome 2:
Experimental probability = 10/61 ≈ 0.164
Absolute difference = |0.164 - 0.167| ≈ 0.003

For outcome 4:
Experimental probability = 9/61 ≈ 0.148
Absolute difference = |0.148 - 0.167| ≈ 0.019

For outcome 6:
Experimental probability = 6/61 ≈ 0.098
Absolute difference = |0.098 - 0.167| ≈ 0.069

For outcome 8:
Experimental probability = 15/61 ≈ 0.246
Absolute difference = |0.246 - 0.167| ≈ 0.079

For outcome 10:
Experimental probability = 13/61 ≈ 0.213
Absolute difference = |0.213 - 0.167| ≈ 0.046

For outcome 12:
Experimental probability = 8/61 ≈ 0.131
Absolute difference = |0.131 - 0.167| ≈ 0.036

The smallest discrepancy between the experimental and expected probability is indeed 0.003.