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...

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) 1 1130.60 2 1210.64 3 1211.25 4 1047.01 5 1135.67 6 1189.19 7 1237.59 8 1164.33 9 1225.51 10 1165.79 APPENDIX