Question

the city of raleigh has 6,300 registered voters. there are two candidates for city council in an upcoming election: brown and feliz. the day before the election, a telephone poll of 200 randomly selected registered voters was conducted. 120 said theyd vote for brown, 73 said theyd vote for feliz, and 7 were undecided. give the sample statistic for the percentage of voters surveyed who said theyd vote for brown. round your answer to the nearest tenth of a percent. % of the surveyed voters said theyd vote for brown. this sample statistic suggests that we might expect of the 6,300 registered voters to vote for brown. round your answer to the nearest person. question help: video message instructor submit question jump to answer

Explanation:

Step1: Calculate the percentage of surveyed voters for Brown

The formula for percentage is $\frac{\text{number of favorable cases}}{\text{total number of cases}}\times100\%$. Here, the number of voters who said they'd vote for Brown is $120$, and the total number of surveyed voters is $200$. So the percentage is $\frac{120}{200}\times100\%$.
$$\frac{120}{200}\times100\%=(120\div200)\times100\% = 0.6\times100\%=60.0\%$$

Step2: Estimate the number of registered voters for Brown

If the percentage of voters for Brown in the sample is $60.0\%$, and the total number of registered voters is $6300$. We use the formula $\text{estimated number}=\text{percentage}\times\text{total number of registered voters}$. So it is $60.0\%\times6300$.
$$60.0\%\times6300=\frac{60}{100}\times6300 = 0.6\times6300=3780$$

Answer:

$60.0\%$ of the surveyed voters said they'd vote for Brown. This sample statistic suggests that we might expect $3780$ of the $6,300$ registered voters to vote for Brown.