Problem

A poll is to be conducted prior to an election to determine the governor of a state. Suppose that it is known that the political party breakdown of likely voters in that state is $41.7 \%$ Democrats, $39.1 \%$ Republicans, and $19.2 \%$ Independents. The pollsters would like to survey 1,247 likely voters stratified by political party affiliation. How many Republicans should be used in the sample?

Solution

Step 1 :Given that the total number of likely voters to be surveyed is 1,247 and the percentage of Republicans is 39.1%, we can calculate the number of Republicans by multiplying the total number of voters by the percentage of Republicans.

Step 2 :Let's denote the total number of voters as \(V\), and the percentage of Republicans as \(P\). The number of Republicans can be calculated as \(R = V \times P\).

Step 3 :Substitute \(V = 1247\) and \(P = 0.391\) into the equation, we get \(R = 1247 \times 0.391\).

Step 4 :Calculate the value of \(R\), we get \(R = 487.577\).

Step 5 :Since the number of people cannot be a decimal, we round \(R\) to the nearest whole number, which is 488.

Step 6 :Final Answer: The number of Republicans that should be used in the sample is \(\boxed{488}\).

From Solvely APP
Source: https://solvelyapp.com/problems/14428/

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