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Answer:
the approximate probability that the insurance company will have claims exceeding the premiums collected is
Step-by-step explanation:
The probability of the density function of the total claim amount for the health insurance policy is given as :
Thus, the expected total claim amount = 1000
The variance of the total claim amount
However; the premium for the policy is set at the expected total claim amount plus 100. i.e (1000+100) = 1100
To determine the approximate probability that the insurance company will have claims exceeding the premiums collected if 100 policies are sold; we have :
P(X > 1100 n )
where n = numbers of premium sold
Therefore: the approximate probability that the insurance company will have claims exceeding the premiums collected is