Let X~N(?,?2), and let Z=(X??)/?. Use Equation (4.25) to

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

ISBN: 9780073401331 38

Solution for problem 19E Chapter 4.5

Statistics for Engineers and Scientists | 4th Edition

Textbook Solutions
2901 Step-by-step solutions solved by professors and subject experts
Get 24/7 help from StudySoup virtual teaching assistants

Statistics for Engineers and Scientists | 4th Edition

4 5 1 258 Reviews

Problem 19E

Let X~N(μ,σ2), and let Z=(X‒μ)/σ. Use Equation (4.25) to show that Z~N(0,1)

Step-by-Step Solution:

Answer:

Step 1 of 1:

In this question, we are asked to prove $Z\sim{}N(0,1)$ , using equation $4.25$ .

Let $X\ \sim{}N(\mu{},\ {\sigma{}}^{2})$ , and let $Z\ =\ \frac{X\ -\ \mu{}}{\sigma{}}$

Equation $4.25$ state that,

Let $X\ \sim{}N(\mu{},\ {\sigma{}}^{2})$ , and let $a\ \ne{}0$ and $b$ be constants. Then,

$aX+b\ \sim{}N(a\mu{}+b,{\ a}^{2}{\sigma{}}^{2})$ ………..(1)

We know that,

$Z\ =\ \frac{X\ -\ \mu{}}{\sigma{}}$

$Z\ =\ \frac{X}{\sigma{}}\ -\frac{\mu{}}{\sigma{}}$ ………(2)

From equation (2), let,

$a\ =\frac{1}{\sigma{}},\ and$ $b\ =\ -\frac{\mu{}}{\sigma{}}\$

Now...

Step 2 of 3

Chapter 4.5, Problem 19E is Solved

Step 3 of 3

Textbook: Statistics for Engineers and Scientists

Edition: 4

Author: William Navidi

ISBN: 9780073401331

Since the solution to 19E from 4.5 chapter was answered, more than 285 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 19E from chapter: 4.5 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. The answer to “Let X~N(?,?2), and let Z=(X??)/?. Use Equation (4.25) to show that Z~N(0,1)” is broken down into a number of easy to follow steps, and 12 words. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This full solution covers the following key subjects: let, show, equation, use. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4.