Question

An insurance company has issued 100 policies. The number of claims filed under each policy follows a Poisson distribution with a mean 2. Assuming that the claims filed by each policyholder are independent of each other, what is the approximate probability that more than 220 claims will be filed by the group of policyholders? B) 0.159 A) 0.079 C) 0.444 D) 0.556 E) 0.921 Question 2-20 An actuary is studying claim patterns in an insurer's book of business. He compiles his findings in the following table: Probability of Claim 0.10 0.08 0.05 0.02 Portion of Business 0.20 0.35 0.30 Tier 0.15 4 Given a claim occurs, calculate the probability the policy is Tier l E) 0.50 D) 0.43 C) 0.40 B) 0.30 A) 0.10

Answer 1

Ans:

1)

mean=200

standard deviation=sqrt(200)=14.14

z=(220-200)/14.14

z=1.414

P(z>1.414)=0.079

Option A is correct.

2)

P(claim)=0.1*0.2+0.08*0.35+0.05*0.3+0.02*0.15=0.066

P(Tier I/claim)=0.1*0.2/0.066=0.30

Option B is correct(0.30)