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IAI Actuarial Core Principles · Actuarial Statistics · Central limit theorem

X ~ Binomial(100, 0.3). Using a normal approximation with continuity correction, P(25 < X ≤ 35) is approximated by the normal probability of which interval for the approximating variable Y?

The interval is 25.5 < Y < 35.5. The event contains the integers 26 to 35, and each integer is represented by an interval of width one around it, so the boundaries are 25.5 and 35.5.

  1. A25 < Y < 35
  2. B24.5 < Y < 34.5
  3. C25.5 < Y < 35.5Correct
  4. D24.5 < Y < 35.5
  5. 25.5 < Y < 34.5

Explanation

The event 25 < X ≤ 35 means X takes the integer values 26, 27, ..., 35. The continuity correction extends the lower end to 25.5 and the upper end to 35.5. Option 24.5 to 35.5 would include X = 25, which is excluded.

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