An organization that offers annuities must construct the yearly payout in light of the likelihood dispersion of the life of the members in the arrangement. Assume the lifetimes of the members are roughly ordinarily conveyed with a mean of 72 years and a standard deviation of 5 years. What extent of the arrangement beneficiaries pass on before they achieve the standard retirement age of 65?A organization that offers annuities must construct the yearly payout in light of the likelihood dissemination of the length of life of the members in the arrangement. Assume the likelihood circulation of the lifetimes of the members is around a typical dispersion with a mean of 68 years and a standard deviation of 3.5 years (Show your workings unmistakably).
a) What extent of the arrangement beneficiaries would get installments past age 75?
b) What extent of the arrangement beneficiaries kick the bucket before they achieve the standard retirement age of 65?
c) Find the age at which installments have stopped for around 86% of the arrangement members.