Question

At the beginning of 2007, the population of a certain state was 55.4% rural and 44.6% urban. Based on past trends, it is expected that 12% of the population currently residing in the rural areas will move into the urban areas, while 20% of the population currently residing in the urban areas will move into the rural areas in the next decade. What was the population distribution in that state at the beginning of 2017? (Round your answers to one decimal place.)

rural	_____%
urban	_____%

Answer 1

We are given here that:
P( Rural 2007) = 0.554,
P( Urban 2007) = 0.446

Also, transition probabilities here are given as:
P(RU) = 0.12, P(RR) = 1 - 0.12 = 0.88
P(UR) = 0.2, P(UU) = 1 - 0.2 = 0.8

Now for 2017, we compute the proportion of rural and urban population here is computed as:

P(Rural 2017) = P( Rural 2007)P(RR) + P( Urban 2007)P(UR)

= 0.554*0.88 + 0.446*0.2 = 0.57672

Therefore Rural: 57.672% is the required proportion here.

Urban: 1 - Rural = 1 - 0.57672 = 0.42328

Therefore Urban: 42.328% is the required proportion here.