Interquartile range of an exponential

EasyRandom Variables Statistics~4m

A service time is exponential and its median is $3$ minutes. What is its interquartile range (the 75th percentile minus the 25th percentile), in minutes? (to 4 decimals)

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Median 3 ⇒ λ = ln(2)/3; then $q_p = -\ln(1-p)/\lambda$ .
$\text{IQR} = q_{0.75} - q_{0.25} = \ln(3)/\lambda = 6 - 1.2451$ .

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4.7549 (± 0.001)

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Interquartile range of an exponential

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