You are given the following information from a life tablI90

You are given the following information from a life tablI90 = 1000 and I93 = 825Deaths are uniformly distributed over each year of age.Calculate the probability that (90) dies between ages 93 and 95.5. (Ans 0.345)

Solution

Using the formulae d_x=q_xl_x , d_x=l_x-l_x+1 and l_x+1=p_xl_x we complete the life table as follows,

We assume that the number of death between ages x and x+1 is uniformly distributed.

Given l₉₀=1000 and l₉₃=825.

From the table l₉₅=600 and l₉₆=360.

Required P[a person aged 90 dies betwen ages 93 and 95.5]

              = (No. of deaths between 93 and 95.5)/(No. of persons aged 90)

              = { (l₉₃-l₉₅)+d₉₅/2 }/1000     (Since deaths are uniform between ages)

              = {825-600+120}/1000

              = 0.345      (Ans.)

x	lx	dx	px	qx
95	600	240	0.6	0.4
96	360	288	0.2	0.8
97	72	72	0.0	1.0