Question

For a life insurance company, it is important to construct life tables (consisting of the probability that a person will survive in the next year, conditional on a person that has been survived up to current). A life insurance company uses life tables to assist calculation of life insurance premium. Assume that the lifetime of randomly selected person is approximately normally distributed with a mean 68 years and a standard deviation 4 year.

A whole life insurance implies that insurance company needs to pay out the death benefit if the insured die, no matter when the death event is happened.  For a group of 10 independent newborn insureds who are currently all under whole life insurances, What is the probability that a randomly selected person will die before 60 years?

Answer 1

let us consider x is the lifetime of a randomly selected person

mean $\mu$ = 68 year

standard deviation $\sigma$ = 4 year

since x is normally distributed with mean  $\mu$ and standard deviation $\sigma$

so P(x< 60) =

60 – 68 P(Z <

P(x< 60) = P(z<-2) =  0.0228 ( from z table )

the probability that a randomly selected person will die before 60 years is 0.0228