Final answer:
The probability that a person dies before reaching the age of 30 is 30%. The probability that a person lives more than 70 years is also 30%, according to the survival distribution function provided.
Step-by-step explanation:
The student is asking about the interpretation and application of a survival distribution function in a life expectancy context. The function s(x), represents the survival probability up to age x. Part (a) and (b) can be answered using this survival distribution.
Part (a)
To calculate the probability that a person dies before reaching the age of 30, we can utilize the complement of the survival function, which is the cumulative distribution function (CDF) for mortality.
Since the survival distribution is s(x) = 1 - x/100, the probability of dying before age 30 is
P(X < 30) = 1 - s(30)
= 1 - (1 - 30/100)
= 30/100
= 0.3 or 30%.
Part (b)
For the probability that a person lives more than 70 years, we look directly at the survival function. The probability of living past age 70 is
P(X > 70) = s(70)
= 1 - 70/100
= 0.3 or 30%.