Use the table to answer the following question.
$$\begin{array} { | c | c | c | }
\hline \text { Age (years) } \mathbf { x } & \text { Number alive at start of year } \mathbf { n } _ { \mathbf { x } } & \mathbf { l } _ { \mathbf { x } } \
\hline 1 & 100 & 1.0 \
\hline 2 & 50 & 0.5 \
\hline 3 & 50 & \boldsymbol { y } \
\hline 4 & 10 & \boldsymbol { z } \
\hline
\end{array}$$
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).

Question

Use the table to answer the following question.
$$\begin{array} { | c | c | c | } 
\hline \text { Age (years) } \mathbf { x } & \text { Number alive at start of year } \mathbf { n } _ { \mathbf { x } } & \mathbf { l } _ { \mathbf { x } } \
\hline 1 & 100 & 1.0 \
\hline 2 & 50 & 0.5 \
\hline 3 & 50 & \boldsymbol { y } \
\hline 4 & 10 & \boldsymbol { z } \
\hline
\end{array}$$
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).

Quizplus · Accepted Answer

To find the missing values of y and z, we need to use the formula for age-specific survivorship rate:
lₓ = (number of individuals alive at the start of the year x) / (number of individuals alive at the start of the year x-1)
Using this formula, we can find the missing values:
y = (number of individuals alive at the start of year 3) / (number of individuals alive at the start of year 2) = 50/100 = 0.5
z = (number of individuals alive at the start of year 4) / (number of individuals alive at the start of year 3) = 10/50 = 0.2
Therefore, the best choice is C, with y = 0.5 and z = 0.2.

Use the Table to Answer the Following Question In the Accompanying Life Table of a Hypothetical Population, What