HW2 - Texas A&M University Department of Mechanical...

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Texas A&M University Department of Mechanical Engineering MEEN 260 Measurement and Instrumentation in Mechanical Engineering Fall 2010 Assignment #2 Due Monday September 20, 2010 Problem 1: (3 points.) For a a very large set of data, the measured mean is found to be 17 with a standard deviation of 1. Assuming the data to be normally (Gaussian) distributed, determine the range within which 75% of the data are expected to fall. Note: There are infinitely many possible answers but three of these are particularly relevant. Determine these three answers. Problem 2: (4 points.) Consider the data set given the Excel spreadsheet associated with Assign- ment #2. There are 200 data points from a simulated temperature measurement experiment. a. Using all the data points, determine the average temperature and standard deviation and esti- mate the true value of temperature with a confidence of 95% b. Repeat Part a using the first 30 data points. What is your conclusion? c. Repeat Part a using the first 10 data points. What is your conclusion? d. Repeat Part a using the first 5 data points. What is your conclusion?
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Solution September 22, 2010 2 Solution Problem 1: Note that we are dealing with a large set of data and the problem statement assumes a Gaussian distribution for this data set. Looking at the probability distribution function (PDF) shown below, we note that what we are asked to do is to find and such that the area under the curve between and is 0.75, meaning that the probability that measurements of fall between and would be 75%. It is clear from the figure that we can choose
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HW2 - Texas A&M University Department of Mechanical...

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