Question

1. maria and daniel are running for 8th grade class president. four students each polled 20 different students to predict the winner of the election. the poll results are shown in the table below. poll | students planning to vote for maria | students planning to vote for daniel 1 | 9 | 11 2 | 10 | 10 3 | 13 | 7 4 | 12 | 8 a total of 180 students will vote in the election. what is the range in the number of votes for ma predicted by these four polls? a. 45 to 117 votes b. 81 to 117 votes c. 90 to 117 votes d. 91 to 117 votes

Explanation:

Step1: Find the proportion for each poll

For each poll, the proportion of students voting for Maria is $\frac{\text{Maria's votes in poll}}{\text{Total polled (20)}}$. Then we multiply this proportion by the total voters (180) to get the predicted votes for Maria.

Step2: Calculate for Poll 1

Proportion: $\frac{9}{20}$, Predicted votes: $\frac{9}{20} \times 180 = 81$

Step3: Calculate for Poll 2

Proportion: $\frac{10}{20}$, Predicted votes: $\frac{10}{20} \times 180 = 90$

Step4: Calculate for Poll 3

Proportion: $\frac{13}{20}$, Predicted votes: $\frac{13}{20} \times 180 = 117$

Step5: Calculate for Poll 4

Proportion: $\frac{12}{20}$, Predicted votes: $\frac{12}{20} \times 180 = 108$

Step6: Find the range

The minimum predicted votes for Maria is 81 (from Poll 1) and the maximum is 117 (from Poll 3). So the range is 81 to 117 votes.

Answer:

B. 81 to 117 votes