Final answer:
The Webster's Plan apportionment formula is used to determine the number of representatives each state should have based on its population.
Step-by-step explanation:
The Webster's Plan apportionment formula is used to determine the number of representatives each state should have based on its population. In this problem, there are four states and a total of 16 representatives. To allocate the representatives using Webster's Plan, we calculate a priority value for each state, which is the ratio of its population to the geometric mean of the lower and upper quotas. The lower quota is the minimum number of representatives a state should have, which is the integer part of its population divided by the total population. The upper quota is the lower quota plus one. We then assign the representatives based on the highest priority values until all the representatives are allocated.
Let's calculate the lower and upper quotas for each state:
- North: 18,200 / (18,200 + 12,500 + 17,800 + 13,400) * 16 = 4.027
- South: 12,500 / (18,200 + 12,500 + 17,800 + 13,400) * 16 = 2.758
- East: 17,800 / (18,200 + 12,500 + 17,800 + 13,400) * 16 = 3.937
- West: 13,400 / (18,200 + 12,500 + 17,800 + 13,400) * 16 = 2.277
Now, let's calculate the priority values:
- North: 18,200 / sqrt(4 * 5) = 4.560
- South: 12,500 / sqrt(3 * 4) = 3.333
- East: 17,800 / sqrt(5 * 4) = 4.218
- West: 13,400 / sqrt(3 * 4) = 3.333
Based on the priority values, we allocate the representatives as follows:
- North: 4 representatives
- South: 3 representatives
- East: 5 representatives
- West: 4 representatives
Therefore, the correct answer is option A) N S E W 4 3 5 4.