A displacement sensor with digital display was used to measuring the displacement of a body impacted by a mass. Relevant sensor data is provided below. Twenty displacement measurements are made, which yield the following: Average measured value 20.00 [mm] Standard deviation of measured values 0.37 [mm] Resolution of sensor display 0.1 [mm] Sensor Accuracy 0.5 [%] of reading A.) If an additional measurement were to be made, calculate the range expected to contain the next measurement with 95% confidence. (i.e. the Precision Interval) B.) Determine the uncertainty for the measured displacement at 95% probability based on all available information.
A displacement sensor with digital display was used to measuring the displacement of a body impacted by a mass. Relevant sensor data is provided below. Twenty displacement measurements are made, which yield the following: Average measured value 20.00 [mm] Standard deviation of measured values 0.37 [mm] Resolution of sensor display 0.1 [mm] Sensor Accuracy 0.5 [%] of reading A.) If an additional measurement were to be made, calculate the range expected to contain the next measurement with 95% confidence. (i.e. the Precision Interval) B.) Determine the uncertainty for the measured displacement at 95% probability based on all available information.
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Question
![A displacement sensor with digital display was used to measuring the displacement of a body impacted by a mass. Relevant sensor data is provided below. Twenty
displacement measurements are made, which yield the following:
Average measured value
20.00 [mm]
Standard deviation of measured values
0.37 [mm]
Resolution of sensor display
0.1 [mm]
Sensor Accuracy
0.5 [%] of reading
A.) If an additional measurement were to be made, calculate the range expected to contain the next measurement with 95% confidence. (i.e. the Precision Interval)
B.) Determine the uncertainty for the measured displacement at 95% probability based on all available information.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F655b22e2-8b5b-4e22-ad56-ac93b8c36c59%2Fbb458cfd-4391-4c05-8f80-92b89ed0573c%2Fhkzfdx8_processed.png&w=3840&q=75)
Transcribed Image Text:A displacement sensor with digital display was used to measuring the displacement of a body impacted by a mass. Relevant sensor data is provided below. Twenty
displacement measurements are made, which yield the following:
Average measured value
20.00 [mm]
Standard deviation of measured values
0.37 [mm]
Resolution of sensor display
0.1 [mm]
Sensor Accuracy
0.5 [%] of reading
A.) If an additional measurement were to be made, calculate the range expected to contain the next measurement with 95% confidence. (i.e. the Precision Interval)
B.) Determine the uncertainty for the measured displacement at 95% probability based on all available information.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
A).
Assume,
- μ be the population mean measurement.
- x be the random variable representing the measurements.
- be the sample mean measurement.
- s be sample standard deviation associated with measurements.
- n be the sample size.
- be the value of t-statistics which corresponds to proportion of area, under the right tail of t-curve with degrees of freedom n-1.
The data mentioned in the question can be written as,
20 measurements are being made, the range for the next measurement with 95% confidence can be given as .
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