Chapter 5.3, Problem 15E

In considering medical insurance for a certain operation, let X equal the amount (in dollars) paid for the doctor and let Y equal the amount paid to the hosp ital. In the past, the variances have been $\mathrm{var}\left(X\right)=8100,\mathrm{var}\left(Y\right)=10,000,$ and $\mathrm{var}\left(X+Y\right)=20,000$.

Due to increased expenses, it was decided to increase the doctor’s fee by $500 and increase the hospital charge Y by 8%. Calculate the variance of $X+500+\left(1.08\right)Y$, the new total claim.