Verified solution · Exam P
This Exam P sample reference tests Density Normalization. This problem normalizes a linearly increasing density and then inverts its CDF. The resulting 80th percentile is √(3.2)=1.78885, which selects choice E.
Independent solution
Setup
Write the density as cx on its support and determine c from total probability.
Model
Integrate the normalized density to obtain the cumulative probability.
Compute
Set the CDF equal to 0.80 and take the positive root within the support.
Answer
The percentile rounds to 1.79.
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Original practice · fully worked
A laboratory response score X has density c for 0<x<2, density 2c for 2≤x<5, and density zero elsewhere, where c is a positive constant. Calculate the 60th percentile of X.
Normalization gives c=1/8, and the lower segment contains probability 0.25. The remaining 0.35 needed to reach 0.60 lies in the upper segment, giving q=3.4 and choice C.
Setup
Normalize the two constant-density segments.
Model
Determine which segment contains the requested percentile.
Compute
Add the lower-segment mass to the probability accumulated in the upper segment.
Answer
The 60th percentile is 3.4.
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ActuaryProof. “SOA Exam P Sample Question #429 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
