Original practice · fully worked
Original variant: resin-strength percentiles
A composite resin's strength index R is normally distributed with a positive mean and coefficient of variation 0.20. Its percentile corresponding to standard-normal score z = 1 is 52. Calculate the value at the symmetric percentile corresponding to z = -1.
- A
34.7 - B
41.6 - C
43.3 - D
52.0 - E
62.4
Answer and calculation
The named percentiles correspond to z = 1 and z = -1, while sigma = 0.20 mu. Solving mu + sigma = 52 gives mu = 43.3333 and sigma = 8.6667, so the lower percentile is 34.6667 and choice A.
Setup
Setup
Translate the coefficient of variation into a relationship between the positive mean and standard deviation.
μσ=0.20⟹σ=0.20μ Model
Model
The 84.1345th percentile has standard score 1, so use its value to solve for the distribution parameters.
52=μ+σ=μ+0.20μ=1.20μ μ=43.3333333,σ=8.6666667 Compute
Compute
The 15.8655th percentile has standard score -1, so evaluate the symmetric lower point.
q0.158655=μ−σ q0.158655=43.3333333−8.6666667=34.6666667 Answer
Answer
The lower resin-strength percentile rounds to 34.7.
q0.158655≈34.7(A) 