Skip to content

IAI Actuarial Core Principles · Actuarial Statistics · Central limit theorem

X is an integer-valued random variable with a distribution well approximated by a normal distribution Y. Which statement gives the correct continuity-corrected approximation of P(12 < X ≤ 20)?

The correct approximation is P(12.5 < Y < 20.5). Because X is an integer, 12 < X ≤ 20 means X takes the values 13 to 20. Each integer k occupies the interval from k − 0.5 to k + 0.5, so the continuous range is 12.5 to 20.5.

  1. AP(11.5 < Y < 20.5)
  2. BP(12.5 < Y < 20.5)Correct
  3. CP(12.5 < Y < 19.5)
  4. DP(12 < Y < 20)
  5. P(13.5 < Y < 20.5)

Explanation

For integer X, 12 < X ≤ 20 is the same as 13 ≤ X ≤ 20. Each integer k is represented by the interval (k − 0.5, k + 0.5), so the range runs from 12.5 to 20.5. The option 11.5 to 20.5 wrongly includes 12, and 12.5 to 19.5 wrongly drops 20.

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.

Practise Central limit theoremFree diagnostic mock

More Central limit theorem questions