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Q.14

Expert-verified
Found in: Page 311

### Introductory Statistics

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

# Find the probability that x falls in the shaded area.

The probability that $x$ falls in the shaded area is: $P\left(2.5\le x\le 5.5\right)=0.3$

See the step by step solution

## Step 1: Given Information

Given in the question that a graph.

We have to find the probability that $x$ falls in the shaded area.

## Step 2: Calculation

From the information, we know that

$f\left(x\right)=\left\{\begin{array}{l}\frac{1}{10}, 0\le x\le 10\\ 0, \text{otherwise}\end{array}\right\$

Let's consider the graph first, Where we obtain that the shaded region is $2.5\le x\le 5.5$.

Therefore, the probability of the shaded region will be,

$P\left(2.5\le x\le 5.5\right)={\int }_{2.5}^{5.5} \frac{1}{10}dx$

$=\frac{1}{10}\left[x{\right]}_{2.5}^{5.5}$

$=\frac{1}{10}\left[5.5-2.5\right]$

$=\frac{3}{10}$

$=0.3$