Verified solution · Exam P
This Exam P sample reference tests Poisson Distribution. This is a Poisson upper-tail calculation with the parameter inferred from the standard deviation. A standard deviation of 2 means the Poisson mean is 4, so complementing the probabilities of zero and one call gives 0.9084 and choice E.
Independent solution
Setup
For a Poisson count, the variance equals the mean. Square the supplied standard deviation to obtain the parameter.
Model
Use the complement of the two excluded low-count outcomes.
Compute
Evaluate the first two Poisson probabilities.
Answer
The upper-tail probability rounds to 0.908.
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Original practice · fully worked
The number of overnight incidents recorded by a monitoring service has a Poisson distribution with variance 3. Its dashboard adds one standing system check to the incident count. Calculate the probability that the displayed count is at most 2.
The Poisson variance gives a mean of 3. A display no greater than two permits at most one actual incident. Adding the zero- and one-incident probabilities gives 0.1991 and choice C.
Setup
Use the Poisson variance to identify its parameter.
Model
Translate the dashboard threshold back to the underlying incident count.
Compute
Add the two qualifying Poisson masses.
Answer
The dashboard is at most two with probability 0.1991.
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ActuaryProof. “SOA Exam P Sample Question #355 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
