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

## Problem 14E Chapter 3.2

Statistics for Engineers and Scientists | 4th Edition

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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

Step 5 of 5

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