Calculus with Applications (10th Edition)

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

Chapter 11 - Probability and Calculus - 11.3 Special Probability Density Functions - 11.3 Exercises - Page 597: 1


a. $\mu=\frac{37}{10}$ b. $\sigma=\frac{7\sqrt 3}{30}\approx0.404$ c. $1.289$

Work Step by Step

We are given $f(x)=\frac{5}{7}; [3;4.4]$ The mean of the distribution: $\mu=\frac{1}{2}(4.4+3)=\frac{37}{10}$ The standard deviation of X is $\sigma=\frac{1}{\sqrt 12}(4.4-3)=\frac{7\sqrt 3}{30} \approx0.404$ One standard deviation above the mean indicates the length of $4.4+0.404=4.804$ $P(T\geq4.804)=\int^{4.804}_{3}\frac{5}{7}dt=\frac{5}{7}t|^{4.804}_{3}\approx1.289$
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