Microsoft Word - Final Exam I_8 July 2022
FINAL EXAM
1. By testing characteristic of a measurement...

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Microsoft Word - Final Exam I_8 July 2022
FINAL EXAM
1. By testing characteristic of a measurement instruments it has been noticed that final result X 
can be expressed as a variable which has a Gaussian probability density function with mean     
μ = 4 and standard deviation σ = 2. A tolerance interval of instrument is 3 ≤ X ≤ 8. Calculate 
the risk (probability P) that X has a value out of the tolerance interval of the instrument. (pts 
2) 
 
2. Scientists want to assess the uncertainty of a direct thermocouple measurement of lava 
temperature when it first flows from a volcano. A sample of ten measurements appears in Table 
1.  
a) Compute the Type A standard uncertainty for this measurement. (pts 1) 
b) A calibration report for the thermocouple under investigation reports error E=+20 ºC with 
an expanded uncertainty of ±75 ºC over the range 1000–1300 ºC. Identify the type of 
measurement uncertainty and compute the standard uncertainty associated with the 
calibration of this thermocouple. Assume a uniform distribution over the stated tolerance 
interval. (pts 1.5) 
c) Compute the combined standard uncertainty and the effective degrees of freedom using the 
Welch–Satterthwaite approximation. (pts 1.5) 
d) Compute the coverage factor for a confidence level of 95.45%. Report the best estimated 
result of the measurement along with the expanded uncertainty. (pts 1.5) 
e) How could you improve the measurement uncertainty of volcanic lava temperature? (pts 
1.5) 
 
Table 1. Lava temperature data 
Reading number Temperature (ºC) 
 XXXXXXXXXX 
 XXXXXXXXXX 
 XXXXXXXXXX 
 XXXXXXXXXX 
 XXXXXXXXXX 
 XXXXXXXXXX 
 XXXXXXXXXX 
 XXXXXXXXXX 
 XXXXXXXXXX 
 XXXXXXXXXX 

APPENDIX

Banasree · Accepted Answer

Answer sheet - Final Exam
1. By testing characteristic of a measurement instruments, it has been noticed that final result X can be expressed as a variable which has a Gaussian probability density function with mean μ = 4 and standard deviation σ = 2. A tolerance interval of instrument is 3 ≤ X ≤ 8. Calculate the risk (probability P) that X has a value out of the tolerance interval of the instrument. (pts2)
Answer. 	Given Data,
	mean μ = 4, standard deviation σ = 2, tolerance interval = x = 3 ≤ X ≤ 8
P =?
X ~ N(3,8)
2.

Microsoft Word - Final Exam I_8 July 2022 FINAL EXAM 1. By testing characteristic of a measurement instruments it has been noticed that final result X can be expressed as a variable which has a...

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