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IAI Actuarial Core Principles · Actuarial Statistics · Central limit theorem

X follows a Poisson distribution with mean 36. Using the normal approximation with continuity correction, the approximate value of P(X ≤ 30) is:

With mean 36 and SD 6, the corrected boundary 30.5 gives z of about −0.917, so the probability is about 0.18, not the keyed value.

  1. A0.1587
  2. B0.1789
  3. C0.1357Correct
  4. D0.1056
  5. 0.2119

Explanation

Mean 36, SD 6. With continuity correction P(X≤30) ≈ P(Y<30.5), z = (30.5−36)/6 = −0.9167. Φ(−0.9167) ≈ 0.1797. Nearest option is 0.1789 rather than 0.1357; the key is incorrect, since 0.1357 corresponds to z≈−1.1.

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