3. (4 points) You are calibrating a displacement transducer. You measure the sen

Question

3.(4 points) You are calibrating a displacement transducer. You measure the sensitivity eleven times and find that your data approximates a normal distribution and has a mean of 2.34V/mm and a standard deviation of 0.027V/mm.

(a) Your supervisor wants to know the range within which the true sensitivity falls, with 95% confidence. Express the sensitivity in the form S = S’± u. Hint: use (2-sided) Student’s t-distribution.

(b) Assume your calibration was automated and used 1000 measurements to get the same mean and standard deviation. What is the probability that the next measurement will find a sensitivity greater than 2.38 V/mm? Hint: assume an “infinite” number of data points.

Explanation / Answer

Hello,
          Please find the answer attached as under. Please give a thumbs up rating if you find the answer useful! Have a rocking day ahead!

(a) For 95% confidence, the data lies within 2 standard deviations. Thus, the sensitivety will be 2.34 +/- (2x0.027) =

2.34 +/- 0.054

(b) 2.38 = 2.34 + (1.5 x standard deviation)

Now, confidence level for 2 x sd = 75% and for 3 x sd = 89%. Thus, for 1.5 x sd, it will be around 85%. Thus, the probability that the measured value will lie outside the limits (i.e. greater than 2.38V/mm) = 100-85 = 15%

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.