Exercise
ABy Admin
May 07'23
Answer
Solution: D
Let X denote the number of deaths next year, and S denote life insurance payments next year. Then [math]S = 50000X [/math], where [math]X \sim \textrm{Bin}(1000,0.014) [/math]. Therefore,
[[math]]
\operatorname{E}(S) = E(50, 000 X ) = 50,000(1000)(0.014) = 700,000
[[/math]]
[[math]]
\operatorname{Var}(D) = \operatorname{Var}(50,000 X ) = 50,000^2 (1000)(0.014)(0.986) = 34,510, 000, 000
[[/math]]
[[math]]
\operatorname{StdDev}(S) = 185,769.
[[/math]]
The 99th percentile is
700,000+185,769(2.326)= 1,132,099,
which rounds to 1,150,000.