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IAI Actuarial Core Principles · Actuarial Statistics · Confidence intervals and prediction intervals

A random sample of 100 motor claims from a Chennai insurer has sample mean ₹24,000 and sample standard deviation ₹5,000. The claim distribution is skewed. Which is the approximate 90% confidence interval for the mean claim size, using z = 1.645?

The interval is ₹23,177.50 to ₹24,822.50. The central limit theorem makes the mean approximately normal, the standard error is 5,000/10 = 500, and the margin is 1.645 × 500 = 822.5 either side of 24,000.

  1. A₹23,177.50 to ₹24,822.50Correct
  2. B₹23,177.50 to ₹24,000
  3. C₹22,355 to ₹25,645
  4. D₹23,918 to ₹24,082
  5. ₹23,020 to ₹24,980

Explanation

By the central limit theorem, the sample mean is approximately normal for n = 100. SE = 5000/10 = 500. Margin = 1.645×500 = 822.5. The interval is 24,000 ± 822.5. The option ±1,645 uses SD/√n wrongly as 1000, and ±980 uses z = 1.96.

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