## Calculus with Applications (10th Edition)

Published by Pearson

# Chapter 11 - Probability and Calculus - 11.1 Continuous Probability Models - 11.1 Exercises - Page 576: 39

#### Answer

a) $P(x \geq 3) \approx 0.268$ b) $P(x \leq 2)\approx 0.414$ c) $P(2 \lt x \lt 3)\approx 0.3178$

#### Work Step by Step

We are given $f(t)=\frac{1}{2\sqrt x}$ for $x$ in $[1,4]$ a) $P(x \geq 3)=\int^{4}_3\frac{1}{2\sqrt x}dx=\frac{1}{2}\int^{4}_3\frac{1}{\sqrt x}dx=x^{\frac{1}{2}}|^4_3 \approx 0.268$ b) $P(x \leq 2)=\int^{2}_1\frac{1}{2\sqrt x}dx=x^{\frac{1}{2}}|^2_1 \approx 0.414$ c. $P(2 \lt x \lt 3)=\int^{3}_2\frac{1}{2\sqrt x}dx=x^{\frac{1}{2}}|^3_2 \approx 0.3178$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.