Verified solution · Exam P
This Exam P sample reference tests Binomial Distribution. For N~Binomial(5,p), E[N²]=5p+20p². Setting this equal to 1.80 gives the admissible root p=0.20, and 5p(1-p)=0.80, so choice A is correct.
Independent solution
Setup
Relate the second moment to the binomial mean and variance.
Model
Insert the binomial formulas and simplify the resulting equation in p.
Compute
Keep the root that lies in the probability interval, then evaluate the variance.
Answer
The variance is 0.80.
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Original practice · fully worked
A batch contains an unknown number n of independently produced parts, each having probability 0.25 of requiring rework. The rework count M has variance 1.50. Calculate E[M²].
The variance equation n(0.25)(0.75)=1.50 gives n=8. Thus E[M]=2 and E[M²]=1.50+2²=5.50, so choice E is correct.
Setup
Use the supplied variance to determine the batch size.
Model
Solve for n and then compute the binomial mean.
Compute
Recover the second moment from variance plus squared mean.
Answer
The second moment is 5.50.
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ActuaryProof. “SOA Exam P Sample Question #567 — Verified Solution.” Verified 2026-07-30.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-30.
