5) You know that you will inherit 20% of your uncle John’s wealth, 30% of your aunt Becky’s wealth and 50% of your parent’s wealth. Since they are not dead yet, their respective wealth is a RV and all we know is that their wealth at death is ~N and independent of each other. John’s wealth is J~N(1000,1002), Becky’s is B~N(2000,3002) and your parents’ wealth is P~N(5000,5002).

Question

5)	You know that you will inherit 20% of your uncle John’s wealth, 30% of your aunt Becky’s wealth and 50% of your parent’s wealth. Since they are not dead yet, their respective wealth is a RV and all we know is that their wealth at death is ~N and independent of each other. John’s wealth is J~N(1000,1002), Becky’s is B~N(2000,3002) and your parents’ wealth is P~N(5000,5002). 
a)	What is the distribution of you total inheritance?

b)	What is the chance you will inherit at least $3000?

c)	You are 40% sure to inherit at most how much?