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Q.15

Expert-verified
Found in: Page 347

### Introductory Statistics

Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208

# $f\left(x\right)$a continuous probability function, is equal to $\frac{1}{3}$and the function is restricted to $1\le x\le 4$. Describe $P\left(x>\frac{3}{2}\right)$.

The required probability is $P\left(x>\frac{3}{2}\right)$ $=0.83$

See the step by step solution

## Step 1: Given Information

$f\left(x\right)$ a continuous probability function is equal to $\frac{1}{3}$.

The function is restricted to $1\le x\le 4$.

We need to describe $P\left(x>\frac{3}{2}\right)$

## Step 2: Calculation

Here $X$ follows a uniform distribution.

The area between $1\le x\le 4$ forms a rectangle with $X$ axis

Here,

$\text{Height}=\frac{1}{3}$

$\text{Base}=4-\frac{3}{2}$

$=\frac{8-3}{2}$

$=2.5$

Therefore, the required probability is,

$P\left(x>\frac{3}{2}\right)=\text{Base}×\text{Height}$

$=\left(2.5\right)×\left(\frac{1}{3}\right)$

$=0.83$