Original practice · fully worked
Original variant: translating a rounded score across years
In year 1, scores are normal with mean 600 and standard deviation 80. A candidate at the 90th percentile has the score rounded to the nearest ten. In year 2, scores have mean 620 and standard deviation 75. Find the percentile of that same rounded score in year 2.
- A
84th - B
85th - C
86th - D
87th - E
90th
Answer and calculation
The year-1 90th-percentile score is about 702.5 and rounds to 700. In year 2 this is z=1.0667, whose CDF is about 0.857, choice C.
Setup
Setup
Convert the year-one 90th percentile to a score using the standard-normal 90th-percentile quantile.
600+80(1.28155)=702.52⟶700 Model
Model
The score is approximately 702.5 and rounds to 700. Standardize 700 under the year-two distribution.
zyear 2=75700−620=1.06667 Compute
Compute
The year-two standard score is approximately 1.0667, giving cumulative probability about 0.857 and hence the 86th percentile.
Φ(1.06667)≈0.857 Answer
Answer
The same rounded score is approximately at the 86th percentile.
86th percentile(C) 