Question

the future lifetime of a newborn is uniformly distributed in the interval (0,120). using the same model, find the probability that a person age 80 will die within the following five years.

Answer 1

The probability that a person age 80 will die within the following five years is 2/3.

Step-by-step explanation:

To find the probability that a person age 80 will die within the next five years, we can use the same uniform distribution model as the future lifetime of a newborn. Since the future lifetime of a newborn is uniformly distributed in the interval (0,120), we can calculate the probability by considering the portion of the interval that represents the next five years for an 80-year-old person.

To do this, we need to find the probability that a person age 80 will live beyond the next five years. The probability that a person will live beyond the next five years is (120-80)/120 = 40/120 = 1/3.

Therefore, the probability that a person age 80 will die within the following five years is 1 - 1/3 = 2/3.

Answer 2

The probability that a person age 80 will die within the following five years is 1/24 or approximately 0.0417.

Step-by-step explanation:

To find the probability that a person age 80 will die within the following five years using the same model as the lifetime of a newborn, we need to consider the cumulative probability distribution function.

Let X be the lifetime of a person measured in years. Since the lifetime is uniformly distributed on the interval (0, 120), the probability density function is f(x) = 1/120 for 0 < x < 120, and 0 elsewhere.

Since we are interested in the probability that a person age 80 will die within the next five years, we can calculate the probability as follows:

P(X <= 85 | X >= 80)

= P(X <= 85) - P(X <= 80)

= 85/120 - 80/120

= 5/120 = 1/24

= 0.0417.