Use the table to answer the following question.

In the accompanying life table of a hypothetical population, what are the missing values for lₓ (y and z)? lₓ = the proportion alive at the start of year (age specific survivorship rate).
A) y = 0.5, z = 0.5
B) y = 1.0, z = 0.5
C) y = 0.5, z = 0.1
D) y = 1.0, z = 0.2

Question

Use the table to answer the following question.

In the accompanying life table of a hypothetical population, what are the missing values for lₓ (y and z)? lₓ = the proportion alive at the start of year (age specific survivorship rate).
A) y = 0.5, z = 0.5 
B) y = 1.0, z = 0.5 
C) y = 0.5, z = 0.1 
D) y = 1.0, z = 0.2

Quizplus · Accepted Answer

We can calculate lₓ by using the formula, lₓ = Dₓ/Nₓ.
For age 0, Dₓ is given as 100 and Nₓ is given as 200.
Thus, l₀ = 100/200 = 0.5
For age 1, we are given l₁ as 0.4 and N₁ as 150.
Thus, D₁ = 150(1-0.4) = 90 and l₁ = 60/150 = 0.4
For age 2, we are given D₂ as 60 and N₂ as zN₁.
Hence, z = D₂/N₂ = 60/(z150) = 0.4/z
Solving for z, we get z = 0.1.
Therefore, the missing values for lₓ are y = 0.5 and z = 0.1, which corresponds to choice C.

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