Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - 8.8 Probability and Integration - Exercises - Page 448: 12



Work Step by Step

The probability for $P(X \geq 20)$ can be computed as: $P(X \geq 20) =\int_{20}^{\infty} \dfrac{1}{r}e^{-x/r} dx \\=\dfrac{1}{r} \lim\limits_{a \to \infty} \int_{20}^{a} e^{-x/r} dx \\=(-1) \lim\limits_{a \to \infty} (\dfrac{1}{e^{a/r}}-e^{-20/8})\\=e^{-20/r}$ We are given that $P(X \geq 20) =\dfrac{1}{2}$ So, we have: $e^{-20/r}=\dfrac{1}{2}\\\dfrac{20}{r}=\ln 2\\r=\dfrac{20}{\ln 2} \approx 28.854$
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