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? The answer needs to be in percent form to the nearest whole number.
To find the experimental probability, we need to divide the frequency of each outcome by the total number of trials. In this case, the total number of trials is 10 + 9 + 6 + 15 + 13 + 8 = 61.
Now, we will calculate the experimental probability for each outcome:
- Experimental probability of 2: 10/61 ≈ 0.164
- Experimental probability of 4: 9/61 ≈ 0.148
- Experimental probability of 6: 6/61 ≈ 0.098
- Experimental probability of 8: 15/61 ≈ 0.246
- Experimental probability of 10: 13/61 ≈ 0.213
- Experimental probability of 12: 8/61 ≈ 0.131
Now, let's find the expected probability for each outcome. Since each face is equally likely, the expected probability for each outcome is 1/6 ≈ 0.167.
The discrepancies between the experimental and expected probabilities are as follows:
- Discrepancy for 2: 0.164 - 0.167 = -0.003
- Discrepancy for 4: 0.148 - 0.167 = -0.019
- Discrepancy for 6: 0.098 - 0.167 = -0.069
- Discrepancy for 8: 0.246 - 0.167 = 0.079
- Discrepancy for 10: 0.213 - 0.167 = 0.046
- Discrepancy for 12: 0.131 - 0.167 = -0.036
The smallest discrepancy in absolute value is 0.003. Converting this to a percentage and rounding to the nearest whole number gives 0%. Thus, the smallest discrepancy is 0%.
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? The answer needs to be in percent form to the nearest thousandth.
To find the experimental probability, we need to divide the frequency of each outcome by the total number of trials. In this case, the total number of trials is 10 + 9 + 6 + 15 + 13 + 8 = 61.
Now, we will calculate the experimental probability for each outcome:
- Experimental probability of 2: 10/61 ≈ 0.164
- Experimental probability of 4: 9/61 ≈ 0.148
- Experimental probability of 6: 6/61 ≈ 0.098
- Experimental probability of 8: 15/61 ≈ 0.246
- Experimental probability of 10: 13/61 ≈ 0.213
- Experimental probability of 12: 8/61 ≈ 0.131
Now, let's find the expected probability for each outcome. Since each face is equally likely, the expected probability for each outcome is 1/6 ≈ 0.167.
The discrepancies between the experimental and expected probabilities are as follows:
- Discrepancy for 2: 0.167 - 0.164 ≈ 0.003
- Discrepancy for 4: 0.167 - 0.148 ≈ 0.019
- Discrepancy for 6: 0.167 - 0.098 ≈ 0.069
- Discrepancy for 8: 0.167 - 0.246 ≈ 0.079
- Discrepancy for 10: 0.167 - 0.213 ≈ 0.046
- Discrepancy for 12: 0.167 - 0.131 ≈ 0.036
The smallest discrepancy in absolute value is 0.003. Converting this to a percentage gives 0.3%. Thus, the smallest discrepancy is 0.3% to the nearest thousandth.
try again
I apologize for the mistake. Let's reevaluate the discrepancies between the experimental and expected probabilities.
Experimental probabilities:
2: 10/61 ≈ 0.164
4: 9/61 ≈ 0.148
6: 6/61 ≈ 0.098
8: 15/61 ≈ 0.246
10: 13/61 ≈ 0.213
12: 8/61 ≈ 0.131
Expected probability for each outcome: 1/6 ≈ 0.167
Now, calculating the discrepancies:
|2 - 0.167| = 0.003
|4 - 0.167| = 0.181
|6 - 0.167| = 0.069
|8 - 0.167| = 0.079
|10 - 0.167| = 0.046
|12 - 0.167| = 0.036
The smallest discrepancy is 0.003 or 0.3% when converted to a percentage to the nearest thousandth. Thank you for your patience.
daz wrong
Let's calculate the discrepancies between the experimental and expected probabilities correctly this time.
Experimental probabilities:
2: 10/61 ≈ 0.164
4: 9/61 ≈ 0.148
6: 6/61 ≈ 0.098
8: 15/61 ≈ 0.246
10: 13/61 ≈ 0.213
12: 8/61 ≈ 0.131
Expected probability for each outcome: 1/6 ≈ 0.167
Discrepancies:
|0.164 - 0.167| = 0.003
|0.148 - 0.167| = 0.019
|0.098 - 0.167| = 0.069
|0.246 - 0.167| = 0.079
|0.213 - 0.167| = 0.046
|0.131 - 0.167| = 0.036
The smallest discrepancy is 0.003. When converted to a percentage to the nearest thousandth, it is 0.3%. Thank you for your patience and I appreciate your understanding.