Final answer:
To perform the apportionment for province G using Hamilton's method, we first calculate the standard divisor, which is the total population of all provinces divided by the number of available federal judges. Province G would initially receive 54 judges based on its population and the standard divisor. Additional judges would be allocated to provinces with the highest fractional remainders if any remain.
Step-by-step explanation:
To use Hamilton's method for apportionment, we need to determine an initial allocation of judges for each province based on population, ensuring none receives less than one judge. The total number of federal judges to be allocated across all provinces is 300. We calculate the initial allocation by dividing the total population of all provinces by the number of available positions to determine the standard divisor. Then, each province's population is divided by this divisor to ascertain the number of positions they should receive initially (quotient). Any excess judges after initial allocation are distributed one by one to the provinces with the largest fractional remainders until all positions are filled.
The total population of all seven provinces is: 25312 + 19734 + 33407 + 29591 + 13288 + 22751 + 31992 = 176075. The standard divisor is the total population divided by the number of judges: 176075 / 300 = 586.92 (rounded to two decimal places). Province G has a population of 31992. When we divide that by the standard divisor (31992 / 586.92), we get approximately 54.48. The initial whole number of judges for province G is then the integer part of this result, which is 54.
After initial allocations are done for all provinces, any leftover judges are apportioned based on the highest remaining fractions. Since we haven't computed this for the other provinces, we can't assign the extra judges just yet. Province G has a fractional remainder of 0.48; depending on the remainders of other provinces, this may or may not result in an additional judge after all are considered.