Casualty Actuarial Society MAS-1 Complete Practice Test 2026

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Using the ILT to price life insurance policies, the lower bound for the number of deaths during a period is given by which expression?

E(N) + z*sqrt(Var(N))

E(N) - z*sqrt(Var(N))

Think of the number of deaths in the period as a quantity with a mean E(N) and a standard deviation sqrt(Var(N)). When we use a normal-approximation idea, outcomes are typically within a band around the mean, extending a certain number of standard deviations in each direction. The lower bound is obtained by subtracting that spread from the mean: E(N) minus z times the standard deviation, where z is chosen from the standard normal distribution for the desired confidence level. This gives E(N) - z * sqrt(Var(N)).

So the lower bound for the number of deaths is E(N) - z*sqrt(Var(N)). For reference, a larger bound on the upper side would be E(N) + z*sqrt(Var(N)). The other expressions don’t reflect this symmetric, standard-deviation-based interval.

E(N) - z*Var(N)

E(N) / (1 + z*sqrt(Var(N)))