A certain scale has an uncertainty of 3 g and a bias of 2

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

Problem 14E Chapter 3.2

Statistics for Engineers and Scientists | 4th Edition

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

Statistics for Engineers and Scientists | 4th Edition

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Problem 14E

A certain scale has an uncertainty of 3 g and a bias of 2 g.

a. A single measurement is made on this scale. What are the bias and uncertainty in this measurement?

b. Four independent measurements are made on this scale. What are the bias and uncertainty in the average of these measurements?

c. Four hundred independent measurements are made on this scale. What are the bias and uncertainty in the average of these measurements?

d. As more measurements are made, does the uncertainty get smaller, get larger, or stay the same?

e. As more measurements are made, does the bias get smaller, get larger, or stay the same?

Step-by-Step Solution:

Step 1 of 5:

Given a scale has an uncertainty of 3g and a bias of 2 g.

Our goal is:

a). A single measurement is made on this scale. We need to find the bias and

     uncertainty in this measurement.

b). Four independent measurements are made on this scale.We have to find the bias

     and uncertainty in the average of these measurements.

c). 400 independent measurements are made on this scale. We have to find the bias

     and uncertainty in the average of these measurements.

d). As more measurements are made, we need to find the uncertainty get smaller, get

     larger, or stay the same.

e).  As more measurements are made, we need to find the bias get smaller, get

     larger, or stay the same.  

a).

Given a single measurement is made on this scale.

Then we have to find the bias and uncertainty in this measurement.

We know that a scale has an uncertainty of 3g and a bias of 2 g.

So the bias is 2 g and the uncertainty is 3 g and

Step 2 of 5:

b).

Here four independent measurements are made on this scale.

Then we have to find the bias and uncertainty in the average of these measurements.

Here the uncertainty is divided into equal parts because the uncertainty in the measurement is normally distributed, but the bias stays same.

Step 3 of 5:

c).

Given 400 independent measurements are made on this scale.

Then we have to find the bias and uncertainty in the average of these measurements.

The uncertainty is

       

Here 20 times smaller than case A.

So the uncertainty is 20 and the bias stays same.

Step 4 of 5

Chapter 3.2, Problem 14E is Solved
Step 5 of 5

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

The full step-by-step solution to problem: 14E from chapter: 3.2 was answered by Patricia, our top Statistics solution expert on 06/28/17, 11:15AM. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4th. This full solution covers the following key subjects: measurements, bias, made, uncertainty, Scale. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The answer to “A certain scale has an uncertainty of 3 g and a bias of 2 g.a. A single measurement is made on this scale. What are the bias and uncertainty in this measurement?________________b. Four independent measurements are made on this scale. What are the bias and uncertainty in the average of these measurements?________________c. Four hundred independent measurements are made on this scale. What are the bias and uncertainty in the average of these measurements?________________d. As more measurements are made, does the uncertainty get smaller, get larger, or stay the same?________________e. As more measurements are made, does the bias get smaller, get larger, or stay the same?” is broken down into a number of easy to follow steps, and 105 words. Statistics for Engineers and Scientists was written by Patricia and is associated to the ISBN: 9780073401331. Since the solution to 14E from 3.2 chapter was answered, more than 248 students have viewed the full step-by-step answer.

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