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Nine independent measurements are made of the length of a
Chapter 3, Problem 13E(choose chapter or problem)
Nine independent measurements are made of the length of a rod. The average of the nine measurements is \(\overline X=5.238\ \mathrm {cm}\), and the standard deviation is \(s=0.081\ \mathrm {cm}\)
a. Is the uncertainty in the value closest to
, or
Explain.
b. Another rod is measured once by the same process. The measurement is Is the uncertainty in this value closest to
, or
? Explain.
Equation Transcription:
Text Transcription:
overline{X}=5.238 cm
s=0.081 cm
Questions & Answers
QUESTION:
Nine independent measurements are made of the length of a rod. The average of the nine measurements is \(\overline X=5.238\ \mathrm {cm}\), and the standard deviation is \(s=0.081\ \mathrm {cm}\)
a. Is the uncertainty in the value closest to
, or
Explain.
b. Another rod is measured once by the same process. The measurement is Is the uncertainty in this value closest to
, or
? Explain.
Equation Transcription:
Text Transcription:
overline{X}=5.238 cm
s=0.081 cm
ANSWER:
Solution:
Step 1 of 2:
Given the average of the nine measurements is .and
The standard deviation is s=0.081 cm.
Our goal is :
a). We need to find the uncertainty in the value 5.238 cm closest to 0.009,0.027,or
0.081 cm.
b). We need to find the uncertainty in this value closest to 0.009,0.027,or
0.081 cm.
a).
Now we have to find the uncertainty in the value 5.238 cm closest to 0.009,0.027,or 0.081 cm.
Then the uncertainty in the average of the nine measurements of the length of the rod is
We know that S =0.081 and n=9.
Therefore the uncertainty in the average of the nine measurements of the length of the rod is
0.027 cm.