Annuity plan participants’ life span: Please answer Questions 1 - 4 based on the following: A company that sells annuities (a form of insurance or investment entitling the investor to a series of annual sums) must base the annual payout on the probability distributions of the length of life of the participants in the plan. Suppose the probability distribution of the lifetime of the participants is approximately a normal distribution with a mean of 68 year and a standard deviation of 4 years. The Z-score of a participant’s life span was Z= -1.33. Approximately what % of participants die before this age? Group of answer choices 90% 10% 81% 9%
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33: X = μ + Zσ = 68 + (-1.33)(4) ≈ 62.68 years. Show more…
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A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. a.What proportion of the plan recipients would receive payments beyond age 75? b.What proportion of the plan recipients die before they reach the standard retirement age of 65? c.Find the age at which payments have ceased for approximately 90% of the plan participants.
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