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Q.5.1

Expert-verifiedFound in: Page 316

Book edition
OER 2018

Author(s)
Barbara Illowsky, Susan Dean

Pages
902 pages

ISBN
9781938168208

Consider the function $f\left(x\right)=\frac{1}{8}$ for $0\le x\le 8$. Draw the graph of $f\left(x\right)$ and find $P(2.5<x<7.5)$.

The graph of the $P(2.5<x<7.5)$ is

The value of the $P(2.5<x<7.5)$ will be $0.625$

Given in the question that the function $f\left(x\right)=\frac{1}{8}$ for $0\le x\le 8$

Here,

$f\left(x\right)=\left\{\begin{array}{l}\frac{1}{8},\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\le x\le 8\\ 0,\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\text{otherwise}\end{array}\right.$

The graph of $f\left(x\right)$ for $P(2.5<x<7.5)$ is drawn below,

Again the required probability will be

$P(2.5<x<7.5)=\text{base}\times \text{height}$

$=(7.5-2.5)\times \left(\frac{1}{8}\right)$

$=5\times \frac{1}{8}$

$=0.625$

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