Page 222 - Probability Demystified

CHAPTER 12 Actuarial Science 211

Mortality Tables

Insurance companies collect data on various risk situations, such as life
expectancy, automobile accidents, hurricane damages, etc. The information
can be summarized in table form. One such table is called a mortality table or
a period life table. You can find one at the end of this chapter. The mortality
table used here is from the Social Security Administration and shows the ages
for males and females, the probability of dying at a specific age, the number
of males and females surviving during a specific year of their lives, and life
expectancies for a given age. The following examples show how to use the
mortality table.

EXAMPLE: Find the probability of a female dying during her 30th year.

SOLUTION:
Based on the mortality table, there are 98,428 females out of 100,000 alive at
the beginning of year 30 and 98,366 females living at the beginning of year 31,
so to find the number of females who have died during year 30, subtract
98,428 98,366 ¼ 62. Therefore, 62 out of 98,428 people have died. Next
find the probability.
number who died during the year
P(dying at age 30Þ¼
number who were alive at the beginning of year 30
62
¼ 0:00063
98,428
(Notice that under the column labeled ‘‘Death probability,’’ the figure
given for 30-year-old females is 0.000624. The discrepancy is probably due to
the fact that computations for this column were based on sample sizes larger
than 100,000 or perhaps it was due to rounding.)
EXAMPLE: On average, how long can one expect a female who is 30 years
old to live?

SOLUTION:

Looking at the table for 30-year-old females, the last column shows a life
expectancy of 50.43 years. This means that at age 30, a female can expect
to live on average another 50.43 years or to age (30 þ 50.43) ¼ 80.43 years.
Interpreting this means that the average of the life expectancies of females
age 30 is 50.43 years. Remember this is an average, not a guarantee.