Worked solution · Exam P
This Exam P sample reference tests Normal Distribution. The two upper-tail probabilities correspond to z-scores 0.449876 and 0.599859. Their 0.149984 difference spans 0.12 units, giving standard deviation 0.800088 and variance 0.640141, so choice B is correct.
Independent solution
Setup
Convert each upper-tail probability to its cumulative standard-normal z-score.
Model
The difference between two standardized thresholds eliminates the unknown mean.
Compute
Solve for the standard deviation and square it.
Answer
The variance rounds to 0.64.
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 daily demand X is normally distributed with positive mean. Its coefficient of variation is 0.25, and its 90th percentile is 132.038789138615. Calculate the mean of X.
CV 0.25 gives sigma=0.25mu. The 90th percentile is therefore mu[1+0.25Phi inverse 0.90]. Equating this to 132.03878914 gives mu=100, so choice C is correct.
Setup
Translate the coefficient of variation into a relation between standard deviation and mean.
Model
Write the normal 90th percentile using its standard-normal quantile.
Compute
Solve the linear equation for the positive mean.
Answer
The mean daily demand is 100.
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
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