Worked solution · Exam P
This Exam P sample reference tests Normal Distribution. A normal median equals its mean. The upper-tail condition places the premium at the 95th percentile, so its excess above the median is z0.95 × 500, or 822.427, which rounds to choice A.
Independent solution
Setup
A normal distribution is symmetric, so its median is its mean.
Model
The stated upper-tail probability makes the premium the 95th percentile of the loss distribution.
Compute
Subtract the median before evaluating the standard-normal quantile.
Answer
The premium exceeds the median loss by approximately 822.
Test the method on unseen problems
30 original univariate random variables problems with complete solutions and wrong-choice analysis. Written for Exam P, not copied from the SOA set. One-time $19 PDF.
Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
A wind farm's hourly output is normally distributed with mean 180 MW and standard deviation 24 MW. An operator chooses a reserve threshold R so that output exceeds R in 10% of hours. Calculate the amount by which R exceeds the median hourly output.
The threshold is the 90th percentile and the median is 180 MW. Their difference is 24z0.90=30.757 MW, so choice B.
Setup
Use normal symmetry to identify the median with the stated mean.
Model
An upper-tail probability of 0.10 places the threshold at cumulative probability 0.90.
Compute
Subtract the median and evaluate the 90th standard-normal quantile.
Answer
The reserve threshold is 30.757 MW above the median.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 387 Exam P univariate random variables practice problems.
Drill the method: Exam P Normal Distribution problems
Keep studying
Work through the related free solutions for this topic, review the formulas you used, or keep every current Exam P solution in one searchable PDF.
