Verified solution · Exam P
This Exam P sample reference tests Exponential Distribution. For a normal or continuous uniform distribution, symmetry makes the median equal to the mean. For an exponential distribution, the median is the mean multiplied by the constant natural logarithm of two. In every case, doubling the mean therefore doubles the median, so choice A is correct.
Independent solution
Setup
Write the median-to-mean relation for each of the three distribution families.
Model
Each median is a fixed multiple of its distribution's mean.
Compute
Replace the mean by twice its former value in the common relation.
Answer
The doubling property holds for the exponential, normal, and continuous uniform distributions.
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Original practice · fully worked
A machine's wear grade G is 1, 4, 7, or 10 with probabilities 0.20, 0.35, 0.25, and 0.20, respectively. Its resale credit is C=100/(G+1) dollars. Calculate the median resale credit.
The cumulative probability of the wear grade first exceeds one half at G=4, so 4 is its unique median. The decreasing credit rule carries that median to 100/(4+1)=20 dollars, and direct ordering of the credit masses confirms choice D.
Setup
Locate where the cumulative wear-grade probability first reaches one half.
Model
The credit is a strictly decreasing function of grade. A unique median maps to the corresponding transformed value even though the ordering reverses.
Compute
Apply the resale-credit rule to grade four.
Answer
The median resale credit is 20 dollars.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 388 Exam P univariate random variables practice problems.
Drill the method: Exam P Exponential Distribution problems · Exam P Normal Distribution problems · Exam P Uniform Distribution problems
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ActuaryProof. “SOA Exam P Sample Question #372 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
