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Q.15

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Introductory Statistics

Found in: Page 347

Book edition OER 2018

Author(s) Barbara Illowsky, Susan Dean

Pages 902 pages

ISBN 9781938168208

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Short Answer

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

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Information

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

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

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

Step 2: Calculation

Here $X$ follows a uniform distribution.

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

Here,

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

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

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

$= 2.5$

Therefore, the required probability is,

$P (x > \frac{3}{2}) = Base \times Height$

$= (2.5) \times (\frac{1}{3})$

$= 0.83$

Most popular questions for Math Textbooks

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