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IAI Actuarial Core Principles · Actuarial Statistics · Central limit theorem

Claim sizes on a motor portfolio have mean Rs 8,000 and standard deviation Rs 6,000. An actuary wants the sample mean of n independent claims to lie within Rs 500 of the true mean with approximate probability 95% (use z = 1.96). What is the smallest n required?

Require 1.96 x 6,000 / sqrt(n) to be at most 500, giving sqrt(n) at least 23.52 and n at least 553.19. Rounding up, the smallest sample size is 554 claims.

  1. A139
  2. B554Correct
  3. C138
  4. D553
  5. 24

Explanation

Need 1.96 x 6,000/sqrt(n) <= 500, so sqrt(n) >= 1.96 x 12 = 23.52. Then n >= 553.19, so n = 554. Option 553 truncates rather than rounding up; 139 uses SD of 3,000 effectively.

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