Question

A report noted that 35% of the voters are in favor of a new infrastructure proposal. a random sample of 15 voters was selected and each was asked whether they preferred the new proposal. what is the expected number of voters who prefer the new proposal?

Answer 1

To find the expected number of voters who prefer the new proposal, multiply the sample size (15) by the proportion of voters who are in favor (35%), resulting in an expectation of 5.25 voters.

Step-by-step explanation:

The student is asking about expectation in probability, which refers to the average outcome one would expect from a repeated experiment over the long run. Since 35% of the voters are in favor of the new infrastructure proposal, and a random sample of 15 voters is selected, to determine the expected number of voters who prefer the new proposal, you multiply the sample size by the probability in favor of the proposal. Therefore, the expected number of voters is 15 (the number of voters sampled) multiplied by 0.35 (the probability that a voter is in favor of the new proposal).

Expected number = Sample Size × Probability

Expected number = 15 × 0.35 = 5.25

So, the expected number of voters in our sample who prefer the new proposal is 5.25.