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Interquartile range of an exponential

EasyRandom VariablesStatistics~4m

A service time is exponential and its median is 33 minutes. What is its interquartile range (the 75th percentile minus the 25th percentile), in minutes? (to 4 decimals)

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  1. Median 3 ⇒ λ = ln(2)/3; then qp=−ln⁡(1−p)/λq_p = -\ln(1-p)/\lambda.
  2. IQR=q0.75−q0.25=ln⁡(3)/λ=6−1.2451\text{IQR} = q_{0.75} - q_{0.25} = \ln(3)/\lambda = 6 - 1.2451.

Answer

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4.7549 (± 0.001)

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Asked at: Citadel, Two Sigma

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