Page 225 - Probability Demystified

214 CHAPTER 12 Actuarial Science

number who died at age 48 451
P(dying at age 48Þ¼ ¼ ¼ 0:00486
number alive at age 48 92,790

2. From the table, a 56-year-old female can expect to live another 26.30
years.

3. From the table, the death rate for a 63-year-old female is 0.010598.
Alternate Solution: At age 63, there are 88,518 out of 100,000 females
alive, and there are 87,580 females alive at age 64. Hence,
88,518 87,580 ¼ 938 females died at age 63; then

number who died at age 63 938
Pðdying at age 63Þ¼ ¼ ¼ 0:010597:
number alive at age 63 88,518

4. At age 43, there are 94,629 males out of 100,000 alive. At age 65, there
are 78,410 males alive, so

number alive at 65 78,410
Pðliving to 65Þ¼ ¼ ¼ 0:8286 or 82:86%
number alive at 43 94,629
5. At 25, there are 98,689 females out of 100,000 alive. At age 60, there
are 90,867 females alive; hence,

number alive at 60 90,867
Pðliving to age 60Þ¼ ¼ 0:921 or 92:1%
number alive at 25 98,689

6. At age 21, there are 98,307 out of 100,000 males alive; hence,

number alive at 21 98,307
P(a male will live to age 21Þ¼ ¼ ¼ 0:98307
total born 100,000

7. At age 20, a female can expect to live 60.16 more years. At age 20, a
male can expect to live 55.04 more years. Hence, 60.16 55.04 ¼ 5.12.
A female can expect to live 5.12 years longer than a male if both are
age 20.
8. At age 2, there are 99,187 males out of 100,000 alive. At age 10, there
are 99,013 males alive; hence, 99,187 99,013 ¼ 174 males age 2 who
will die before age 10. This is out of 99,187 males alive at age 2.

9. There are 99,084 females out of 100,000 alive at age 16. There are
95,464 females alive at age 50. Hence,