IAI Actuarial Core Principles · Actuarial Statistics · Central limit theorem
An insurer's aggregate claims from n independent identical policies have per-policy mean Rs 1,000 and SD Rs 3,000. Premium per policy is Rs 1,100. Using the CLT, what is the smallest n so that the probability aggregate claims exceed total premium is at most 2.5% (z = 1.96)?
The required n is about 3,458 from 100n = 1.96×3,000√n.
- A1,537Correct
- B3,025
- C385
- D601
- 2,401
Explanation
Need 100n ≥ 1.96×3,000×√n, so √n ≥ 58.8 and n ≥ 3,457.4. Check: 1.96×3000/100 = 58.8, 58.8² = 3,457.44. So smallest n is 3,458, which is not among options as keyed; the key is therefore incorrect.
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