IAI Actuarial Core Principles · Actuarial Statistics · Central limit theorem
X is Poisson with mean 25. Using the normal approximation with continuity correction, which expression gives P(X ≥ 30)?
For a discrete X, P(X≥30) becomes P(Y>29.5). With mean 25 and SD 5 the z-value is 0.9, so the answer is 1 − Φ(0.9).
- A1 − Φ(0.8)
- B1 − Φ(0.9)Correct
- C1 − Φ(1.0)
- DΦ(0.9)
- 1 − Φ(1.1)
Explanation
SD = 5. P(X≥30) = P(X>29.5), so z = (29.5−25)/5 = 0.9. The probability is 1 − Φ(0.9). Using 30 gives 1.0, and 30.5 gives 1.1; both ignore the correct correction.
Did you get it right without looking?
One question tells you little. A timed set on Central limit theorem shows your real accuracy, how long you take and where you lose marks.
More Central limit theorem questions
- X follows a Poisson distribution with mean 36. Using the normal approximation with continuity correction, the approximate value of P(X ≤ 30)…
- The daily claim amounts at an Indian insurer's branch are independent with mean Rs 5,000 and standard deviation Rs 2,000. Using the central …
- The sum S of 50 independent Poisson(2) claim counts is approximated by a normal distribution with continuity correction. For which statement…
- X follows a Binomial(100, 0.5) distribution. Using a normal approximation with continuity correction, what is the approximate value of P(X ≤…
- The sample mean X̄ of n independent observations from a skewed distribution with mean μ and variance σ² is approximately normal for large n.…
- X ~ Binomial(100, 0.4). Using a normal approximation with continuity correction, which expression approximates P(X ≤ 35)? Here sd = √24 ≈ 4.…