Two types of insurance claims are made to an insurance company. For each type, the number of claims follows a Poisson distribution and the amount of each claim is uniformly distributed as follows:

Type of Claim	Poisson Parameter [math]\lambda [/math] for Number of Claims in one year	Range of Each Claim Amount
I	12	(0, 1)
II	4	(0, 5)

The numbers of claims of the two types are independent and the claim amounts and claim numbers are independent.

Calculate the normal approximation to the probability that the total of claim amounts in one year exceeds 18.

• 0.37
• 0.39
• 0.41
• 0.43
• 0.45

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.