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. Twentydisplacement measurements are made, which yield the following:Average measured value20.00 [mm]Standard deviation of measured values0.37 [mm]Resolution of sensor display0.1 [mm]Sensor Accuracy0.5 [%] of readingA.) 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). Assume, μ be the population mean measurement. x be the random variable representing the…

Answered: A displacement sensor with digital…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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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

Step 1

A).

Assume,

μ be the population mean measurement.
x be the random variable representing the measurements.
$x$ be the sample mean measurement.
s be sample standard deviation associated with measurements.
nbe the sample size.
$t_{\frac{α}{2}}$ be the value of t-statistics which corresponds to proportion of area, $\frac{α}{2}$ under the right tail of t-curve with degrees of freedom n-1.

The data mentioned in the question can be written as, $n = 20, x = 20 a n d s = 0.37$

20 measurements are being made, the range for the next measurement with 95% confidence can be given as $x \pm t_{\frac{α}{2}} s \sqrt{1 + \frac{1}{n}}$ .

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