Environmental Engineering Reference
In-Depth Information
and
ν
Y
= 23, determine the value of
Z
that is
exceeded with 5% probability. What is the
expected value of
Z
?
categories of data, evaluate whether the hypoth-
esis of log normality is supported at the 5% sig-
nificance level.
10.3.
Contaminant concentration data from an appar-
ently normal distribution show a mean of 50 mg/l
and a standard deviation of 10 mg/l. (a) Esti-
mate the probability that the concentration will
exceed 60 mg/l; and (b) estimate the concentra-
tion of the pollutant that is likely to be exceeded
10% of the time.
Category
range (mg/l)
1
[0, 1.0]
2
(1.0, 1.5]
3
(1.5, 2.5]
4
(2.5, 5.0]
5
(5.0, ∞]
10.4.
Concentration data that are measured in mg/l
follow a log-normal distribution, where the mean
and standard deviation of the natural log-
transformed data are 1.5 and 1.0, respectively. (a)
Estimate the mean, standard deviation, and
skewness of the concentration measurements;
(b) What is the probability of the measured con-
centration exceeding 10 mg/l?; and (c) How
would the estimated exceedance probability in
Part (b) be affected if the measured data were
assumed to have a normal distribution?
10.8.
Concentration measurements (in mg/l) derived
from samples over a 50-month period are as
follows:
0.18
3.28
1.23
1.02
2.24
3.90
7.82
1.95
1.42
0.50
1.70
2.46
0.46
0.84
1.86
1.01
8.20
2.25
4.49
1.13
0.51
1.24
3.45
38.00
0.64
0.94
5.07
2.11
1.06
10.28
1.88
4.98
2.70
1.06
2.59
0.96
0.50
5.45
2.22
8.56
10.5.
reports indicate that pollutant concentrations
in a lake are observed to be in the range of
0-30
μ
g/l. Estimate the pollutant concentra-
tion that is likely to have an exceedance rate
of 5%.
0.33
1.46
1.31
3.81
2.26
3.76
9.10
0.33
1.84
0.68
use the Kolmogorov-Smirnov statistic to assess
the hypothesis that these samples are drawn
from a log-normal distribution with a (natural
log) mean of 0.6 and a standard deviation of 1.0.
10.6.
Water-quality samples at a single monitoring
station in a lake yielded the results shown in
Table 10.13. Compare the observed distribution
to a log-normal distribution with a natural log
mean of 0.60 and a standard deviation of 1.00,
and make a visual assessment of the level of
agreement.
10.9.
Monthly samples show the following measured
concentrations in mg/l:
30.10
1.74
2.52
1.13
0.43
2.56
1.22
0.49
1.71
0.71
3.91
0.79
0.26
0.60
2.17
10.7.
An analyst asserts that the water-quality samples
in Example 10.6 are drawn from a log-normal
distribution with a natural log mean of 0.60 and
a standard deviation of 1.00. using the following
0.37
2.02
1.39
0.96
1.23
0.92
4.57
0.16
1.77
6.86
3.08
3.52
2.36
2.14
0.99
TABLE 10.13. Measurements of Contaminant Concentration in a Lake
Sample
Concentration (mg/l)
Sample
Concentration (mg/l)
Sample
Concentration (mg/l)
1
1.02
11
1.24
21
2.15
2
2.18
12
8.70
22
9.33
3
4.88
13
4.17
23
0.74
4
1.29
14
1.76
24
1.51
5
1.21
15
0.84
25
0.65
6
2.56
16
7.35
26
2.63
7
2.73
17
0.45
27
14.36
8
5.18
18
5.71
28
2.59
9
0.62
19
1.32
29
0.72
10
1.60
20
0.81
30
0.59
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