This Exam P sample reference tests Pareto Distribution. Invert the Pareto distribution at probabilities 0.30 and 0.70. Their quantiles differ by about 93, corresponding to choice B.
Original variant: spread between two latency quantiles
A network’s peak latency L has survival function P(L>x)=(100/x)² for x at least 100 milliseconds. Measure the gap from the lower quartile to the upper quartile.
A 50.00 ms
B 73.21 ms
E 84.53 ms
D 100.00 ms
C 115.47 ms
Variant answer in brief
The quantile is 100/√(1-p). The 75th and 25th percentiles are 200 and 115.470, a difference of 84.530 ms.
Setup
Setup
Write the latency distribution from its survival function and denote the percentile corresponding to probability p.
FL(x)=1−(x100)2
Model
Model
Solve the survival equation for the percentile, then apply the resulting reciprocal-square-root formula at probabilities 0.25 and 0.75.
ℓp=1−p100
Compute
Compute
The upper quartile is 200 ms and the lower quartile is 115.470 ms, so their difference is 84.530 ms.
ℓ0.75−ℓ0.25=200−0.75100=84.529946
Answer
Answer
Therefore the interquartile latency spread is 84.53 ms, corresponding to choice E.
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