An insurer's portfolio contains 2000 one-year life insurance policies. Half of them are characterized by a payment b_1= 1 and a probability of dying within 1 year of q_1 = 1%. For the other half, we have b_2=2 and q_2=5%. Use the Central Limit Theorem to determine the minimum safety loading, as a percentage to be added to the net premium to ensure that the probability that the total payment exceeds the total premium income is at most 5%.
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