×
Log in to StudySoup
Get Full Access to Statistics - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Statistics - Textbook Survival Guide

The lengths of two components will be measured several

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 20E Chapter 3.2

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 | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

4 5 1 353 Reviews
13
3
Problem 20E

The lengths of two components will be measured several times. The uncertainty in each measurement of the length of the first component is σ1= 0.02 cm, and the uncertainty in each measurement of the length of the second component is σ2 = 0.08 cm. Let denote the average of the measurements of the first component, and let denote the average of the measurements of the second component. The total length of the two components will be estimated with the quantity

a. Find the uncertainty in the total length if the first component is measured 4 times and the second component is measured 12 times.

b. Find the uncertainty in the total length in terms of n if the first component is measured n times and the second component is measured 16 − n times.

c. Determine the best way to allocate 16 measurements between the components by determining the value of n that minimizes the uncertainty.

Step-by-Step Solution:

Answer

Step 1 of 4</p>

Uncertainty means standard deviation of the measurements

The uncertainty in the length of the first component is

The uncertainty in the length of the second component is

Let denote the average of the measurements of the first component

Let denote the average of the measurements of the second component

The total length of the components will be estimated with the quantity

Step 2 of 4</p>

a) We need to find the uncertainty if the first component is measured 4 times and

     The second component is measured 12 times

     

               =

               =

               =0.0251

Step 3 of 4

Chapter 3.2, Problem 20E is Solved
Step 4 of 4

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

The full step-by-step solution to problem: 20E from chapter: 3.2 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. The answer to “The lengths of two components will be measured several times. The uncertainty in each measurement of the length of the first component is ?1= 0.02 cm, and the uncertainty in each measurement of the length of the second component is ?2 = 0.08 cm. Let denote the average of the measurements of the first component, and let denote the average of the measurements of the second component. The total length of the two components will be estimated with the quantity a. Find the uncertainty in the total length if the first component is measured 4 times and the second component is measured 12 times.________________b. Find the uncertainty in the total length in terms of n if the first component is measured n times and the second component is measured 16 ? n times.________________c. Determine the best way to allocate 16 measurements between the components by determining the value of n that minimizes the uncertainty.” is broken down into a number of easy to follow steps, and 154 words. This full solution covers the following key subjects: component, uncertainty, times, length, measured. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Since the solution to 20E from 3.2 chapter was answered, more than 545 students have viewed the full step-by-step answer.

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

The lengths of two components will be measured several

×
Log in to StudySoup
Get Full Access to Statistics - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Statistics - Textbook Survival Guide
×
Reset your password