Calculus with Applications (10th Edition)

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

Chapter 11 - Probability and Calculus - Chapter Review - Review Exercises - Page 602: 21


a. $\frac{6}{5}$; b. $-\frac{31}{20}$ c. $\frac{27}{50}$

Work Step by Step

We are given $f(x)=\frac{1}{10}$ for x in $[10,20]$ a. $P(X\leq12)=\lim\limits_{a \to -\infty}\int^{12}_{a}\frac{1}{10}dx=\lim\limits_{a \to -\infty}(\frac{1}{10}x)|^{12}_{a}=\lim\limits_{a \to -\infty}(\frac{6}{5}-\frac{1}{10}a)=\frac{27}{50}$ b. $P(X\geq\frac{31}{2})=\lim\limits_{b \to \infty}\int^{b}_{\frac{31}{2}}\frac{1}{10}dx=\lim\limits_{b \to \infty}(\frac{1}{10}x)|^{b}_{\frac{31}{2}}=\lim\limits_{b \to \infty}(\frac{1}{10}b-\frac{31}{20})=-\frac{31}{20}$ c. $P(10.8 \leq X \leq 16.2)=\int^{16.2}_{10.8}\frac{1}{10}dx=\frac{1}{10}x|^{16.2}_{10.8}=\frac{1}{10}$
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