IAI Actuarial Core Principles · Actuarial Statistics · Central limit theorem
A health insurer has 2,500 independent policies. The number of claims per policy per year is Poisson with mean 0.2. Using the CLT, the approximate probability that the total number of claims lies between 480 and 520 inclusive, ignoring continuity correction, is closest to (Φ(0.894)=0.8145, Φ(1.0)=0.8413, Φ(1.414)=0.9213, Φ(1.789)=0.9633):
The probability is about 0.629. The total claim count has mean and variance 500, so 480 to 520 is ±0.894 standard deviations, and 2Φ(0.894) − 1 = 0.629.
- A0.6290Correct
- B0.8413
- C0.8145
- D0.2580
- 0.9266
Explanation
Total is approximately normal with mean 500 and variance 500, SD 22.36. Limits are ±20, so z = ±0.894. Probability = 2×0.8145 − 1 = 0.6290. 0.8145 forgets the two-sided nature.
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