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: 11


$e^{-3/2} \approx 0.22331$

Work Step by Step

The probability for $P(X \geq 12)$ can be computed as: $P(X \geq 12) =\int_{12}^{\infty} \dfrac{1}{8}e^{-x/8} dx \\=\dfrac{1}{8} \lim\limits_{a \to \infty} \int_{12}^{a} e^{-x/8} dx \\=(-1) \lim\limits_{a \to \infty} (\dfrac{1}{e^{a/8}}-e^{-12/8})\\=e^{-3/2}\\ \approx 0.22331$
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