Q.5. Floods in a stream have the mean 600 m3 /s and the standard deviation 400 m3 /s. Please answer the following questions assuming normal distribution. a) What is the probability that the flood flow any year exceeds 700 m3 /s? b) What is the 100-year flood discharge?
Q.5. Floods in a stream have the mean 600 m3 /s and the standard deviation 400 m3 /s. Please answer the following questions assuming normal distribution. a) What is the probability that the flood flow any year exceeds 700 m3 /s? b) What is the 100-year flood discharge?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
100%
Q.5. Floods in a stream have the mean 600 m3
/s and the standard deviation 400 m3
/s. Please
answer the following questions assuming normal distribution.
a) What is the probability that the flood flow any year exceeds 700 m3
/s?
b) What is the 100-year flood discharge?
Transcribed Image Text:Table 1. Standard Normal Distribution
A
A = S(z)dz
0 z
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.0
0.09
0.5000 0.4960 0.4920 0.4880 0.4840 0.4801
0.4761 0.4721 0.4681 0.4641
0.0
0.1
0.2
0.3
0.4602 0.4562 0.4522 0.4483
0.4207
0.3821 0.37830.3745
0.4443 0.4404 0.4364
0.4052 0.40130.3974 0.39360.3897
0.3669 0.3632 0.3594 0.3557 0o.3520 0.3483
0.4325 0.4286 0.4247
0.3859
0.416 0.4129
0.4090
0.4
0.5
0.6
0.3446 0.3409 0.3372 0.33360.3300 0.3264 0.3228 03192 0.3156 0.312I
0.3085 0.3050 0.3015
0.2743 0.2709 0.2676 0.2643 0.26II0.2578 0.2546 0.25140.2483 0.2451
0.2946 0.29120.2877 0.2843
0.2810 0.2776
0.7
0.8
0.9
0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.22060.21770.2148
0.2119 0.2090 0.2061 0.2033 0: 200s 0.1977 0.1949 a. 19220.1894 0.1867
0.18410.1814 0.1788 0.1762 0.1736 0.1711 0.16850. 1660 0.1635 0.161I
10
0.1587 0.1 562 0.1539 0.ISIS O.1492 0.1469 0.14460.1423 0.1401 0.1379
1.1
1.2
1.3
0.1357 0.13350.1314 0.1292 0.1271 0.12SI 0.12300.12100.I190 0.1170
0.11510.1I1310.1120.109) 0.1075 0.10560.10380. 1020 0.1003 0.0985
0.09680.0951 0.0934 0.0918 0.09010.08850.0869 0.08530.ON3S0.023
1.4
1.5
1.6
0.08080.0793 0.0778 0.0764 a.0749 0.07350.0721 0.07080.0694 0.068I
0.06430.0630 0.0618 0.0606 0.0594 0.0582
0.0571
0.0s59
0.0668 0.0655
0.054 0.0537 0.0526 0.0s16 O.0505
0.04850.0475 0.0463 0.0455
1.7
1.8
1.9
0.0446 0.0436 0.0427 0.0410.0409 0.0401
0.01590.0351
0.0287
0.03920.0384 0.037S 0.0367
0.0301 0.0294
0.02740.0268 0.0262 0.0256 o.02 30 0.0244a.0239 0.0233
0.03440.0336 0.0329 0.0322 o.03140.0307
0.0281
2.0
0.0228 0.0222 0.0217 0.0212 o.02070.02o2 0.0197 0.0192 0.01880.0183
0.01 79 0.0174 0.0170 0.0166 Q.0162 0.0158 0.0154 0.01 sp 0.0146 0.0143
0.039 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.01160.011) 0.0110
6.0107 0.0104 0.0102 0.0099 0.0096 0.0094
2.1
22
0.00910.0O89 0.00870.0084
2.4
2.5
2.6
0.0082 0.0080 0.0078 0.0075 0.00730.0071
0.0062 0.0060 0.0059 0.0057 0.00Ss0.0054
0.00690.0068 0.0066 0.0064
0.0049 0.0048
0.0052 0.0051
0.00470.00450.0044 0.0043 0.0041 0.0040 0.00390.00380.00370.0036
2.7
2.8
2.9
0.0035 0.0034 0.0033 0.0032 0.00JI
0.0026 0.00250.0024 0.0023 0.0023 0.0022
0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.001s 0.0015 0.0014 0.0014
0.0030 0.0029 0.0028 0.0027 o0.0026
0.0021 0.0021 0.0020 0.0019
3.0
0.po130.00130.00130.00120.0012 0.0011 0.001I 0.00110.0010 0.0010
3.I
3.2
3.3
0.000 0.000s0.00070.0007
0.0005 0.000s 0.000S
0.00050.00os 0.0005 0.00040.0004 0.0004 0.0004 0.00040.0004 0.000
0.00100.0009 0.0009 0.0009 0.0008 0.0008
0.0007
0.0007 0.0006
0.00060.0006 0.0006 0.0006
3.4
3.5
3.6
0.0003 0.00O0.0003 0.000) 0.0003 0.0003 0.00030.00030.0003 0.0002
0.0002 0.0002 0.0002 0.0002 o.0002 0.0002 0.0002 o0002 0.0002
0.00020.0002 0.0001
0.0002
0.00010.0001
0.0001 0.0001 0.0001 0.0001 0.0001
0.0001 0.00o1 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
0.0001
0.0001 0.000
3.7
3.8
3.9
0.0001
0.0001 0.0001 0.0001 a.0001
0.0000
0.0000
0.0001
0.0001 0.0001
0.0001
0.00000.0000 0.0000 0.0000
0.00000.0000
0.00000.000
0.00
0.02
0.03
0.04
0.05
0.04
0.07
0.0a
0.0
0.01
Transcribed Image Text:Table 2. t (STUDENT) distribution MI
P
to
0.45
0.40
0.35
0.20
0.15
Q.10
0.05
0.025
0.01
0.005
0.158
0.142
0.137
0.325
0.289
0.277
0.510
0.445
0.424
1.376
1.061
0.978
1.963
1.386
1.250
3.078
1.886
1.638
6.314
2.920
2.353
12.71 31.82
4.303
6.965
3.182
4.541
63.66
9.925
5.841
0.134
0.132
0.131
0.271
0.267
0.265
0.414
0.408
0.404
0.941
0.920
0.906
1.190
1.156
L.134
1.533
1.476
1.440
2.132
2.015
1.943
2.776
2.571
2.447
3.747
3.365
3.143
4.604
4.032
3.707
0.130
0.130
0.129
0.263
0.262
0.261
0.402
0.399
0.398
0.896
0.889
0.883
1.119
1.108
1.100
1,415
1.397
1.383
1.895
1.860
1.833
2.365
2.306
2.998
2.896
2.821
3.499
3.355
3.250
2.262
10
0.129
0.260
0.397
0.179
1.093
1.372
1.12
2.228
2.764
3.169
0.260
0.259
0.259
0.396
0.395
0.394
0.876
0.873
0.70
1.088
1.083
1.079
1.363
1.J56
1.J50
1.796
1.782
ו1.77
2.201
2.179
2.160
2.718
2.68
2.650
3.106
3.055
3.012
D
0.129
0.128
0.128
%3D
13
0.258
0.258
0.258
0.393
0.393
0.392
0.868
0.866
0.865
1.076
1.074
1.071
1.345
1.341
1.337
2.977
2.947
2.921
14
15
16
0.128
0.128
0.128
1.761
1.753
1.746
2.145
2.131
2.120
2.624
2.602
2.583
0.128
0.127
0.127
0.257
0.257
0.257
0.192
0.392
0.391
0.863
0.862
0.861
1.069
1.067
1.066
1.333
1.330
1.J28
1.740
1.734
1.729
2.110
2.101
2.093
2.567
2.552
2.539
17
2.898
2.878
2.861
19
20
0.127
0.257
0.391
0.860
1.064
1.325
1.725
2.086
2.528
2.845
21
22
23
0.127
O.127
0.127
0.257
0.256
0.256
0.19
0.390
0.390
1.063
1.061
1.060
1.323
1.321
1.319
721.ו
1.717
1,714
2.080
2.074
2.069
2.S18
2.S0
2.500
2.831
2.819
2. 807
0.SE
25
26
0.127
0.127
0.127
0.256
0.256
0.256
0.390
0.390
0.390
0.857
0.856
0.856
1.059
1.058
1.058
1.318
1.316
1.315
1.711
1.708
1.706
2.064
2.060
2.056
2.492
2.485
2.479
2.797
2.787
2.779
27
28
29
0.127
0.127
0.127
0.256
0.256
0.256
0.389
0.389
0.389
0.855
0.855
0.854
1.057
1.056
1.055
1.314
1.313
1.311
1.703
1.701
1.699
2.052
2.04
2.045
2.473
2.467
2.462
2.771
2.763
2.756
30
0.127
0.256
0.389
0.854
1.055
1.310
1.697
2.042
2.457
2.750
40
60
120
0.126
0.126
0.126
0.126
0.255
0.254
0.254
0.253
0.388
0.387
0.386
0.385
0.85
0.48
0.845
O.842
1.030
1.046
1.041
1.036
1.303
1.296
1.289
1.282
1.684
1.671
1.658
1.645
2.021
2.000
1.980
1.960
2.42)
2.390
2.358
2.326
2.704
2.660
2.617
2.576
0.45
0.40
0.35
0.20
0.1S
0.10
0.05
0.025
0.01
0.005
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