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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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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 Fall '08
 LANGARI
 Mechanical Engineering, Statistics, Normal Distribution, Standard Deviation, Mean, data points

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