12.6. A general concept in interpreting measurements of material is the following: We let wthe observed measurement,

12.6. A general concept in interpreting measurements of material is the following: We let w¼the observed measurement, x ¼ the ‘‘true’’ measurement, and y¼the error of measurement

(which may be þ or ). Then w¼ xþy. Since x and y are independent we may use (12.9) with k ¼ 2. Also if the measurement is ‘‘unbiased’’ then my¼0. Suppose mx¼115.0, sx¼2.0, sy¼0.5mm. Assuming that x and y are normally distributed, describe the distribution of the observed measurement w. How influential was sy? (Take note that although x ¼ wy, we could not use sx¼[sw 2þsy 2]1=2 because w and y are not independent. In fact, this equation would give more variation in true dimension than in the measured dimension!)