Verified solution · Exam P
This Exam P sample reference tests Continuous Random Variables. The first density segment contains probability 0.40, so the median lies in the next segment. Accumulating another 0.10 at density 0.30 requires one-third of a year beyond 0.5, giving a median of 5/6 = 0.833333 year and choice B.
Independent solution
Setup
A continuous median m satisfies F(m) = 0.5. First locate the density segment in which the cumulative probability reaches one-half.
Model
Because 0.40 is below one-half, continue through the following segment, where the density is constant at 0.30.
Compute
Set the segment-specific cumulative distribution equal to one-half and solve.
Answer
The median lifetime rounds to 0.83 year.
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Original practice · fully worked
The time R, in hundreds of operating hours, until a greenhouse sensor requires recalibration has density 0.30 for 0 ≤ R ≤ 1, density 0.20 for 1 < R ≤ 3, density 0.10 for 3 < R ≤ 6, and zero elsewhere. Calculate the median recalibration time.
The first interval contributes probability 0.30. Accumulating the remaining 0.20 at density 0.20 takes one more unit, so the median is 2.0 hundreds of hours and choice C.
Setup
Confirm that the stated pieces form a probability density and identify the cumulative mass at each breakpoint.
Model
The first interval contains 0.30 probability, so the 50th percentile occurs in the second interval.
Compute
Solve the median equation inside that interval.
Answer
The median is 2.0 hundreds of operating hours, or 200 hours.
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ActuaryProof. “SOA Exam P Sample Question #708 — Verified Solution.” Verified 2026-07-30.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-30.
