IAI Actuarial Core Principles · Actuarial Statistics · Random sampling and sampling distributions
Claim amounts for a motor portfolio have mean Rs 8,000 and standard deviation Rs 6,000. Using the central limit theorem, what is the approximate probability that the average of 100 independent claims exceeds Rs 8,900? (Phi(1.5)=0.9332, Phi(1)=0.8413, Phi(0.15)=0.5596)
The probability is about 0.0668. The sample mean is approximately normal with standard error 600, so Rs 8,900 is 1.5 standard errors above the mean, and the upper tail probability beyond 1.5 is 0.0668.
- A0.0668Correct
- B0.1587
- C0.4404
- D0.0228
- 0.5596
Explanation
The standard error is 6000/10 = 600. Then z = (8900-8000)/600 = 1.5, so P(Z>1.5) = 1-0.9332 = 0.0668. Option 0.4404 uses the standard deviation 6000 instead of the standard error (z=0.15), and 0.1587 would correspond to z=1.
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