Question

1. Read Chapter 6 pp 142 – 147 in Khisty and Mohammadi (2001).
2. The concentration of lead (Pb) in parts per million (ppm) found in the surficial soils throughout the town of Herculaneum Missouri are given in Table 1 (USEPA 2009) and provided in the end of this description. Use Excel® to perform the following analyses of these data, and report your results in an executive summary. The figures and tables should follow the executive summary. (Units of concentration 1 ppm = 1 mg/l)
A. Construct a histogram (number of observations versus concentration interval) for these data using a 50 ppm-interval and a range from 0 to 800 ppm for your plot. Be sure to properly and completely label and caption your figures. See the ASCE guidelines for help.
B. Calculate the lead concentration sample mean (μ), standard deviation (σ), coefficient of variation (c.o.v.) (δ) and the range (minimum and maximum) for these data. Also, calculate the lognormal standard deviation (Xi, ξ) and the lognormal mean (Lambda, λ). Report them in a table. Properly number and caption the table.
C. Use Excel® to perform your calculations and to construct a lognormal “cumulative” frequency” distribution (CDF). Use a range of concentration beginning with 1 mg/l and increasing by 1 mg/l ending at 1,000 mg/l. It is recommended to watch the video tutorial regarding lognormal distribution.
D. Construct a probability density function (PDF) for the lead concentrations using Excel®.
E. The clean-up action level for lead in soils is 300 mg/l per the US Environmental Protection Agency (US EPA). Calculate the probability that some sites in Herculaneum will need to be remediated (cleaned up) because of excessive lead concentrations.
F. The clean-up action level for lead in soils is 100 mg/l per the Minnesota State Legislature. If this action level is adopted in Herculaneum, what is the probability that a site will need to be cleaned based on the lead data presented in this study.
G. Include a brief discussion of the cost to perform a lead clean up per acre of surface area. You will need to search and provide references to support your cost analysis. Discuss the values and their meaning in your executive summary.

Sample Numbers and Pb (ppm):
1 738
2 727
3 596
4 565
5 526
6 510
7 471
8 463
9 441
10 430
11 410
12 406
13 394
14 390
15 387
16 378
17 371
18 367
19 365
20 362
21 361
22 355
23 351
24 348
25 344
26 335
27 334
28 333
29 323
30 318
31 315
32 307
33 304
34 299
35 298
36 297
37 289
38 276
39 276
40 274
41 272
42 271
43 270
44 261
45 258
46 258
47 252
48 249
49 248
50 245
51 245
52 244
53 239
54 233
55 233
56 233
57 232
58 231
59 228
60 228
61 226
62 226
63 225
64 225
65 224
66 224
67 220
68 218
69 218
70 218
71 217
72 216
73 210
74 210
75 210
76 203
77 202
78 199
79 199
80 198
81 197
82 196
83 195
84 195
85 194
86 193
87 193
88 191
89 189
90 188
91 187
92 184
93 183
94 183
95 182
96 182
97 181
98 180
99 178
100 176
101 175
102 175
103 173
104 170
105 169
106 169
107 166
108 166
109 166
110 163
111 163
112 163
113 162
114 161
115 160
116 160
117 159
118 158
119 157
120 156
121 156
122 156
123 156
124 156
125 155
126 155
127 153
128 153
129 152
130 151
131 151
132 150
133 149
134 148
135 148
136 148
137 147
138 146
139 146
140 144
141 144
142 143
143 142
144 141
145 141
146 141
147 140
148 140
149 139
150 137
151 136
152 135
153 135
154 134
155 134
156 133
157 131
158 130
159 129
160 129
161 129
162 127
163 125
164 125
165 124
166 124
167 124
168 123
169 123
170 122
171 122
172 121
173 120
174 120
175 120
176 120
177 119
178 119
179 119
180 118
181 118
182 116
183 116
184 115
185 114
186 113
187 112
188 110
189 107
190 107
191 106
192 106
193 105
194 104
195 102
196 101
197 101
198 100
199 100
200 100
201 99
202 98
203 98
204 98
205 98
206 97
207 96
208 95
209 95
210 95
211 95
212 93
213 92
214 91
215 90
216 90
217 89
218 89
219 88
220 88
221 87
222 87
223 86
224 86
225 86
226 84
227 84
228 84
229 83
230 81
231 80
232 80
233 79
234 78
235 78
236 78
237 77
238 77
239 77
240 76
241 75
242 74
243 73
244 73
245 73
246 73
247 72
248 71
249 69
250 69
251 68
252 67
253 67
254 67
255 66
256 66
257 66
258 65
259 65
260 64
261 64
262 63
263 63
264 62
265 61
266 60
267 60
268 59
269 58
270 56
271 56
272 56
273 55
274 55
275 54
276 54
277 53
278 53
279 53
280 53
281 50
282 50
283 50
284 50
285 46
286 46
287 45
288 45
289 43
290 42
291 41
292 39
293 39
294 38
295 37
296 36
297 35
298 34
299 32
300 32
301 30
302 29
303 29
304 27
305 25
306 24
307 24
308 18
309 18
310 9

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Probability Functions: Log Normal Distributions

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