Verified solution · Exam P
This Exam P sample reference tests Normal Distribution. This problem transfers a known normal percentile to a higher percentile while retaining the same mean and standard deviation. The 80th-percentile information implies standard deviation about 1.996, and the resulting 90th percentile is 9.278, which rounds to choice C.
Independent solution
Setup
Represent each percentile through its standard-normal score.
Model
Use the supplied mean and 80th percentile to recover the scale.
Compute
Apply the 90th-percentile standard-normal score using the recovered standard deviation.
Answer
The 90th percentile rounds to 9.28.
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Original practice · fully worked
Calibration score A follows a normal model centered at 100. Score B follows another normal model with center 100 and a standard deviation 1.5 times as large as A's. The 90th percentile of A is 112. Calculate the 10th percentile of B.
Complementary normal percentiles have opposite standardized displacements. B's displacement is 1.5 times A's 12-point displacement, so its 10th percentile is 100-18=82 and choice A.
Setup
Write A's upper-percentile displacement from the shared mean.
Model
Scale that displacement for B and use normal symmetry between the 90th and 10th percentiles.
Compute
B's lower-percentile displacement has magnitude 1.5 times twelve and points below the mean.
Answer
The 10th percentile of B is 82.
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ActuaryProof. “SOA Exam P Sample Question #378 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
