Answer:
a. Pr(a randomly selected sophomore student who would vote for Summer) = 0.14
b. Pedro would win the election by a margin of 6 votes
Step-by-step explanation:
Based on the pre-election polling,
Number of students at Preston = 486
Number of sophomore students = 130
Number of non- sophomore students = 486 - 130 = 356
Let us assume that all students of Preston High School will participate in the election.
1. For Summer,
i. 53% of sophomores plan to vote for Summer. So that,
53% of 130 = [tex]\frac{53}{100}[/tex] × 130
= 68.9
≅ 69
The number of sophomore students that will vote for Summer is 69.
ii. The number of non-sophomores that would vote for Summer = (356 - number of those that would vote for Pedro)
= 356 - 185
= 171
2. For Pedro,
i. The number of sophomore students that would vote for Pedro = (130 - number that would vote for Summer)
= 130 - 69
= 61
ii. 52% of non- sophomores will vote for Pedro. So that;
52% of 356 = [tex]\frac{52}{100}[/tex] × 356
= 185.12
≅ 185
a. Pr(a randomly selected sophomore student who would vote for Summer)
= [tex]\frac{69}{486}[/tex]
= [tex]\frac{23}{162}[/tex]
= 0.14198
≅ 0.14
b. Considering the number of students to vote for each candidate,
Summer = 69 + 171 = 240
Pedro = 61 + 185 = 246
Pedro would be expected to win the election by a margin of 6 votes.
