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

Chapter 3, Problem 14E

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QUESTION:

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?

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QUESTION:

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?

ANSWER:

Step 1 of 5

(a)

If a single measurement is made, the bias is 2 g , and the uncertainty is 3 g.

Step 2 of 5

(b)

If four independent measurements are made, the bias in the average of these measurements is 2 g , and the uncertainty is,

\({\sigma _X} = \frac{\sigma }{{\sqrt n }}\)

\({\sigma _X} = \frac{3}{{\sqrt 4 }}\)

\({\sigma _X} = 1.5\;{\rm{g}}\)

Step 3 of 5

(c)

If four hundred independent measurements are made, the bias in the average

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