Problem

The table to the right shows four states, their 2010 populations, and their number of seats in a particular branch of government, which has a total of 441 seats. For state $C$, find the standard quota. Use the value 310 million for the total population. Explain whether each state is relatively under- or overrepresented in the House.
\begin{tabular}{ccc}
\hline State & Population & Seats \\
\hline A & $18,603,000$ & 26 \\
B & $12,547,000$ & 17 \\
C & $11,995,000$ & 18 \\
D & $12,651,000$ & 17 \\
\hline
\end{tabular}
Select the correct choice below and fill in the answer box to complete your choice. (Round to two decimal places as needed.)
A. State $\mathrm{C}$ is overrepresented because its standard quota of $\square$ is lessthan its number of representatives, 18 .
B. State $\mathrm{C}$ is underrepresented because its standard quota of $\square$ is morethan its number of representatives, 18 .

Answer

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Answer

Final Answer: \(\boxed{17.06}\). State C is overrepresented because its standard quota of 17.06 is less than its number of representatives, 18.

Steps

Step 1 :The standard quota for a state is calculated by multiplying the total number of seats by the ratio of the state's population to the total population. In this case, the total number of seats is 441 and the total population is 310 million. The population of state C is 11,995,000.

Step 2 :Calculate the standard quota for state C using the formula: \(\frac{{\text{{State C Population}}}}{{\text{{Total Population}}}} \times \text{{Total Seats}}\). Substituting the given values, we get \(\frac{{11995000}}{{310000000}} \times 441\), which equals approximately 17.06.

Step 3 :Compare the standard quota with the number of representatives state C has. State C has 18 representatives.

Step 4 :If the standard quota is less than the number of representatives, then state C is overrepresented. If the standard quota is more than the number of representatives, then state C is underrepresented.

Step 5 :The standard quota for state C is approximately 17.06, which is less than its number of representatives, 18. Therefore, state C is overrepresented.

Step 6 :Final Answer: \(\boxed{17.06}\). State C is overrepresented because its standard quota of 17.06 is less than its number of representatives, 18.

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