To find the range in the number of votes for Alyssa predicted by the four polls, we first need to calculate the total number of votes predicted for Alyssa based on the poll results.
From the given data, we have the following votes for Alyssa from each poll:
- Poll 1: 16
- Poll 2: 12
- Poll 3: 14
- Poll 4: 15
To find the total votes predicted for Alyssa from the polls, we can sum these values:
\[ 16 + 12 + 14 + 15 = 57 \]
Now let's calculate the total number of votes predicted for James from the polls:
- Poll 1: 9
- Poll 2: 13
- Poll 3: 11
- Poll 4: 10
Summing these values gives:
\[ 9 + 13 + 11 + 10 = 43 \]
Now we can calculate the total votes in the polls which is the sum of votes for both Alyssa and James:
Total votes in polls = Votes for Alyssa + Votes for James = 57 + 43 = 100
Since there are a total of 200 students that will vote in the election, we can determine the proportion of votes for Alyssa based on the percentage represented by the polls:
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Proportion of votes for Alyssa: \[ \text{Proportion for Alyssa} = \frac{57}{100} = 0.57 \] This means if 200 students vote, the predicted votes for Alyssa would be: \[ 200 \times 0.57 = 114 \]
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Proportion of votes for James: \[ \text{Proportion for James} = \frac{43}{100} = 0.43 \] This means if 200 students vote, the predicted votes for James would be: \[ 200 \times 0.43 = 86 \]
Now, to find the maximum and minimum number of votes Alyssa could get based on the polls (assuming translating the current percentages into whole numbers) we can do the following in regards to adjustments needed due to rounding and excess to reflect a full class of students:
Resistance and variability would have to be accounted for to predict:
- Lower bound for Alyssa might be if a greater percentage went for James from the total rounds.
- Upper estimate would be the same affirmation.
The next step is to estimate accordingly the predictions based on the given options:
Calculating different scenarios on min-max rounds:
- If Alyssa had the lower range in polling:
- 57 is the number she gets proportionally.
- The highest rounds from variance and poll would hover around the
0.57computed making upper limits toward how high they estimated everywhere else.
From the results collected much would have you check ranges: The possible inequalities were shown by a representative feature:
Range prediction:
- Minimum tickets fetched remained to 96
- Maximum potential scaled down nesting into more skew by projection alongside shifted claims at 128.
Based on valid digit match-up to this model:
Thus the range predictive is given as C. 96 - 128.