Final answer:
The hospital's case-mix index for the year is approximately 1.449.
Step-by-step explanation:
To calculate the hospital's case-mix index, you need to divide the sum of the total relative DRG weights by the total number of discharges for the year. In this case, the sum of the total relative DRG weights is 15,192 and the total number of discharges is 10,471. Therefore, the case-mix index would be 15,192 divided by 10,471, which equals approximately 1.449.