You are given:

1. The number of claims follows a Poisson distribution.
2. The number of claims and claim severity are independent.
3. The severity distribution is:

Claim Size	Probability
5	0.60
40	0.35
60	0.05

Calculate the expected number of claims needed so the total cost of claims is within 5% of the expected with probability 0.90.

• 511
• 726
• 1083
• 2044
• 3126

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

Key: D

For the severity distribution, we have [math] \mu_X = 20 [/math] and [math] \sigma_X^2 = 355 .[/math] The standard for full credibility is

[[math]] \left( \frac{1.645}{0.05}\right)^2 (1 + CV_s^2) = \left( \frac{1.645}{0.05} \right)^2(1 + \frac{355}{20^2}) = 2043.05, [[/math]]

round up to 2044.

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