When calculating premiums on life insurance products insurance companies often use life tables that enable the probability of a person dying in any age interval to be calculated.

The following data obtained from New Zealand Abridged Period Life Table: 2014-2016 gives the number out of 100,000 New Zealand-born females and males who are still alive during each five-year period of life between age 20 and 60 (inclusive).

	Number alive at exact age
Exact age (years)	Out of 100,000 female born	Out of 100,000 males born
20	99,288	99,031
25	99,128	98,685
30	98,949	98,312
35	98,726	97,899
40	98,427	97,381
45	97,934	96,649
50	97,157	95,548
55	95,933	93,853
60	94,162	91,352

a. What is the probability that a New Zealand-born female will reach the age of 30?

b. What is the probability that a New Zealand-born female will reach the age of 45?

c. What is the probability that a 20-year-old New Zealand-born female will reach the age of 30?

d. What is the probability that a 20-year-old New Zealand-born female will reach the age of 40?

e. A 30-year-old New Zealand-born female has purchased a term life policy that will pay her estate a million dollars if she dies within five years. What is the probability that the insurance company will pay her estate this amount?

f. Repeat (a) to (e) for New Zealand-born males.