We denote by t the age of a person when he/she dies, ignoring the population tha

Question

We denote by t the age of a person when he/she dies, ignoring the population that lives beyond 100 years. In other words, we have {0 lessthanorequalto t lessthanorequalto 100). It has been determined that the lifespan can be defined by a function a(t) = 3e - 9t^2(100-t)^2, 0 lessthanorequalto t lessthanorequalto 100 You will notice that integral^100_0 a(t) dt = 1. This means that the probability that a person dies between 50 and 60 is integral^60_50 a(t)dt = 0.1874. This is shown by the red shaded area below What is the probability that a person is alive at 60?

Explanation / Answer

We see that the distribution is normally distributed with mean = 50

Hence, probability that person is alive at 50 =1 - [ Cumulative probability till 60] =

1 - [P(dies till 50) + p(50-60) ]= 1- [0.5+0.1874] = 0.3126

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