Question

Three sample surveys are taken about an upcoming election. In the first sample, 65 out of 80 people plan to vote. In the second sample, 77 out of 100 people plan to vote. In the third sample, 28 out of 35 people plan to vote. To the nearest percent, what is the best estimate of the percentage of people who plan to vote in the upcoming election based on the sample surveys?

Answer 1

To find the best estimate of the percentage of people who plan to vote based on the three sample surveys, we will first calculate the proportion of people who plan to vote in each sample and then find the overall percentage.

1. First survey: \[ \text{Percentage} = \left( \frac{65}{80} \right) \times 100 = 81.25% \]

2. Second survey: \[ \text{Percentage} = \left( \frac{77}{100} \right) \times 100 = 77% \]

3. Third survey: \[ \text{Percentage} = \left( \frac{28}{35} \right) \times 100 = 80% \]

Now, we'll average these percentages. First, we sum the percentages: \[ 81.25 + 77 + 80 = 238.25 \]

Next, we divide by the number of surveys (3) to get the average: \[ \text{Average percentage} = \frac{238.25}{3} \approx 79.4167% \]

Rounding this to the nearest percent gives us: \[ \text{Final estimate} = 79% \]

Thus, the best estimate of the percentage of people who plan to vote in the upcoming election based on the sample surveys is \( \boxed{79%} \).