Question

1. in a public opinion poll, 624 people from a sample of 1,100 indicated they would vote for a specific candidate. how many votes can the candidate expect to receive from a population of 40,000?

Explanation:

Step1: Determine the proportion of voters in the sample

The proportion of people who voted for the candidate in the sample is the number of favorable responses (624) divided by the sample size (1,100). So the proportion \( p=\frac{624}{1100} \).

Step2: Apply the proportion to the population

To find the expected number of votes in the population of 40,000, we multiply the population size by the proportion from the sample. Let \( V \) be the expected number of votes. Then \( V = 40000\times\frac{624}{1100} \).

First, simplify the calculation:
\( 40000\times\frac{624}{1100}=\frac{40000\times624}{1100}=\frac{400\times624}{11}=\frac{249600}{11}\approx22690.91 \) (we can also do the calculation as \( 40000\div1100\times624=\frac{400}{11}\times624\approx36.36\times624\approx22690.91 \))

Answer:

The candidate can expect to receive approximately \(\boldsymbol{22691}\) votes (or approximately 22690.91 votes, depending on rounding). If we round to the nearest whole number, it's 22691.