Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 11 - Probability and Calculus - 11.1 Continuous Probability Models - 11.1 Exercises - Page 576: 31


a. $P(0\leq X \leq 1) \approx 0.098$ b. $P(1 \leq X \leq 3) \approx 0.096$ c. $P(X\geq 2)\approx 0.092$

Work Step by Step

We find: a. $P(0\leq X \leq 1)$ $=\frac{1}{2}\int^{1}_{0}e^{-x/2}dx$ $=-\frac{1}{4}e^{-\frac{1}{2}x}|^{1}_{0}$ $\approx 0.098$ b. $P(1 \leq X \leq 3)$ $=\frac{1}{2}\int^{3}_{1}e^{-x/2}dx$ $=-\frac{1}{4}e^{-\frac{1}{2}x}|^{3}_{1}$ $\approx 0.096$ c. $P(X\geq 2)$ $ =\int^{\infty}_{2}\frac{1}{2}e^{-x/2}dx$ $=\frac{1}{2}\int^{\infty}_{2}e^{-x/2}dx$ $=-\frac{1}{4}e^{-\frac{1}{2}x}|^{\infty}_{2}$ $\approx 0.092$
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