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IAI Actuarial Core Principles · Actuarial Statistics · Basic univariate distributions and generating samples

The monthly claim amount X (in thousand rupees) for a motor portfolio of an Indian insurer is modelled as Normal with mean 50 and standard deviation 8. Using Φ(1.25) = 0.8944, what is P(X > 60)?

The probability is 0.1056. Standardising gives z = (60 − 50)/8 = 1.25, and the upper tail probability is 1 − Φ(1.25) = 1 − 0.8944. The figure 0.8944 is the opposite tail, and doubling would give a two-sided probability.

  1. A0.1056Correct
  2. B0.8944
  3. C0.2112
  4. D0.0668
  5. 0.1587

Explanation

Standardise: z = (60 − 50)/8 = 1.25. P(X > 60) = 1 − Φ(1.25) = 1 − 0.8944 = 0.1056. The value 0.8944 is the lower tail, which is the wrong tail, and 0.2112 wrongly doubles it as if two-sided.

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