In a stationary population of 120, 000 lives, the number of deaths is 2000 annually. The complete expectation of life for a 40-year-old is 30 years. 60% of the population is under age 40.
What is the average age at death for an individual in this population?
What is the average age at death for an individual who dies before age 40?
I know the answer for the average age at death for an individual in this population is supposed to be 60. I am not sure how to get this though. Is it because if I start with 120000 and subtract 2000 each year that an individual lives but then multiple its by a percentage, thats how I get it?
For the average age at death for an individual that dies before 40, I know the answer should be 20. Do I get this by doing the same as the first part but multiple my 60% because 60% is under age 40?
Thank you
Average life expectancy at birth is $\frac{120000}{2000} = 60$ because of the stationary population
The number of people aged over $40$ is $0.4 \times 120000 = 48000$
Since they live an average of $30$ years beyond $40$, there must be $\frac{48000}{40} = 1600$ of them arriving at age $40$ each year, and a total of $1600 \times (30+40)=112000$ of them in the population, of which $48000$ are over $40$ and $64000$ are under $40$ at any one time
So $2000-1600=400$ are born each year who will die before $40$ and there are $120000 -112000 = 8000$ of them in the population at any one time. The average life expectancy at birth for an individual who dies before age $40$ is therefore $\frac{8000}{400}= 20$