IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Graduation and graduation tests
At one age, a graduated rate gives expected deaths of 25 and 36 deaths were observed. Using the normal approximation, what is the standardised deviation, and is it unusual at the 5% level?
The standardised deviation is (36 - 25) divided by the square root of 25, which equals 2.2. This exceeds 1.96, so the deviation is unusually large at the 5% level, indicating a poor fit at this age.
- A2.2; unusual, as it exceeds 1.96Correct
- B1.4; not unusual
- C2.2; not unusual, as it is below 2.58
- D11.0; highly unusual
- 0.44; not unusual
Explanation
Standardised deviation = (36 - 25)/sqrt(25) = 11/5 = 2.2. Dividing by the expected deaths (25) instead of its square root would give 0.44, which is wrong. Since 2.2 exceeds 1.96, it is unusual at 5%.
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