SOA Exam P Practice Q22

The claim amount, X, for a home insurance policy is a random variable with the following probability function:
P(X=0) = 0.3, P(X=1) = 0.1, P(X=2) = 0.6.
The premium for the policy is equal to 120% of the expected claim amount.
Calculate the approximate probability that the total claims on 64 independent policies exceed the total premium collected.
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