Question

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 $P(2.5<x<7.5)$.

Short answer

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

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

Step-by-step solution

Given information

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

Solution

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,

Solution

Again the required probability will be

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

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

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

$=0.625$