Verified solution · Exam P

SOA Exam P Sample Question #339 Solution

This Exam P sample reference tests Binomial Distribution. This is the standard deviation of a binomial count. With n=500 and p=0.12, the variance is 500(0.12)(0.88)=52.8, so the standard deviation is √(52.8)≈7.27 and choice A.

Independent analysis by ActuaryProof · reviewed August 4, 2026

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Independent solution

How to solve this Binomial Distribution question

Setup

Independent returns with a common probability produce a binomial count.

N\sim\operatorname{Binomial}(500,0.12)

Model

Use the binomial variance formula and then take its square root.

\operatorname{Var}(N)=np(1-p)

\operatorname{SD}(N)=\sqrt{np(1-p)}

Compute

Substitute the item count and return probability.

\operatorname{Var}(N)=500(0.12)(0.88)=52.8

\operatorname{SD}(N)=\sqrt{52.8}=7.266360849

Answer

The standard deviation rounds to 7.27.

\boxed{7.27\quad\text{(A)}}

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Error diagnosis

Why the other letters tempt

These notes identify the calculation error associated with each wrong letter when that error is reproducible.

BThe value 7.75 is approximately √(np)=√(60), omitting the required factor 1-p from the binomial variance.
CA standard deviation of 12.75 would imply variance about 162.6, which exceeds np=60. A binomial variance np(1-p) cannot exceed np.
DThe value 20.98 is approximately √(n(1-p))=√(440), omitting the success-probability factor p.
EThe value 52.80 is the binomial variance. Standard deviation is its square root.

Original practice · fully worked

Original variant: audit score volatility

An audit runs 240 independent checks, each passing with probability 0.35. The audit score adds 5 points for every pass and subtracts 2 points for every failed check. Calculate the standard deviation of the total audit score.

A
7.389
B
51.724
C
54.600
D
64.156
E
2675.400

Variant answer in brief

If N is the pass count, the total score is 5N-2(240-N)=7N-480. The pass-count standard deviation is sqrt[240(0.35)(0.65)], and scaling by 7 gives 51.724, choice B.

Setup

Represent the number of passing checks by a binomial variable.

N\sim\operatorname{Binomial}(240,0.35)

Model

Rewrite the total score as an affine function of the pass count.

S=5N-2(240-N)=7N-480

\operatorname{SD}(S)=7\operatorname{SD}(N)

Compute

Calculate the pass-count variance and apply the score scale.

\operatorname{Var}(N)=240(0.35)(0.65)=54.6

\operatorname{SD}(S)=7\sqrt{54.6}=51.72426897

Answer

The standard deviation of the total score is approximately 51.724 points.

\boxed{51.724\quad\text{(B)}}

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ActuaryProof. “SOA Exam P Sample Question #339 — Verified Solution.” Verified 2026-07-31.

Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.

How to solve this Binomial Distribution question

Setup

Model

Compute

Answer

All 718 Exam P sample solutions in syllabus order

Why the other letters tempt

Original variant: audit score volatility

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam P solutions

Turn this solution into a complete study sequence

Cite this solution