The number of claims for a portfolio of insureds has a negative binomial distribution with parameters r = 10 and β = 3. The size of claims has pdf f(x) = 0.5 f1(x) + 0.5 f2(x) where f1 is the Pareto pdf with (α = 3, θ = 2,000) and f2 is the Pareto pdf with (α = 3, θ = 10,000). Claim counts and claim sizes are independent. Using the normal approximation, determine the probability that aggregate claims will be greater than 100,000.

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