MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Civil and Environmental Engineering
1.017 Computing and Data Analysis for Environmental Applications
Practice Quiz 1, 2003
Problem 1 (Descriptive Statistics)
During the manufacture of links in a chain, they are sampled at random and the tensile
strength measured. Characterize the set of 12 maximum load values given below by
plotting or computing the following descriptive statistics:
Histogram
Sample cumulative distribution function (CDF)
Sample mean
Sample standard deviation
Sample median
6.2
3.8
5.0
4.8
3.4
5.3
3.9
6.4
4.2
5.5
5.2
4.0
Use the sample CDF to estimate the probability of a link having a tensile strength less
than or equal to 4.
Solution:
Histogram:
Mean = 4.8
Standard Deviation = 0.96
Median = 4.9
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CDF:
P(strength<=4) = 4/12 = 0..33
Problem 2 (Combinations and Virtual Experiments)
A geologic formation consists of 9 layers: 4 shale, 3 sandstone, and 2 limestone.
We
presume that these layers were laid down at random.
Now suppose that we drill a
borehole through the top 3 layers. What is the probability that these sampled layers are all
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 Spring '05
 GeorgeKocur
 Normal Distribution, Standard Deviation, Environmental Engineering, Probability theory, Cumulative distribution function, Lake A

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