please solve with steps 5 A fund has been established for th

please solve with steps.

(5) A fund has been established for the purpose of insuring 11,060 lives with identical mortality profiles. For each life, you are given: (i) The probability of an accidental death is 0.01, and the probability of a non accidental death is 0.09 (ii) If death is accidental, the claim amount is 10. For other causes of death, the claim amount is 1. Calculate the amount needed in the fund so that the probability, using the normal approximation, is 95% that the fund will be sufficient to pay the death claims. (Ans 2279)

Solution

X= Amount per death

Y = Total amount

E(x) = (0.01)(10) + (0.09)(1) = 0.19

E(x^2) = (10)^2(0.01) + (1)^2(0.09) = 1.09

Var(X) = E(X^2) - (E(X))^2 = 1.09 - (0.19)^2 = 1.0539

Y = 11060*X

E(Y) = 11060*0.19 = 2101.4

Var(Y) = 11060*Var(X) = 11060*1.0539 = 11656.134

s.d(Y) = 107.96

p = 0.95 means z = 1.645

z = (Y-mean)/s.d

1.645 = (Y-2101.4)/107.96

So Y = 2279