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AGS520S - AGRICULTURAL STATISTCS - 2ND OPP - JAN 2023 |
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nAmlBIA UnlVERSITY
OF SCIEnCE Ano TECHnOLOGY
FACULTYOF HEALTH,NATURAL RESOURCESAND APPLIEDSCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: BACHELOR OF AGRICULTURAL MANAGEMENT
QUALIFICATION CODE: 07BAGR
LEVEL: 5
COURSE CODE: AGS520S
COURSE NAME: AGRICULTURAL
STATISTICS
SESSION: JANUARY 2023
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
SUPPLEMENTARY/SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER
J. AMUNYELA
MODERATOR:
Mr A. ROUX
INSTRUCTIONS
1. Answer ALL the questions in the booklet provided.
2. Show clearly all the steps used in the calculations.
3. All written work must be done in blue or black ink and sketches must
be done in pencil.
ATTACHMENT: Formula sheet, t-table, z-tables, chi-square table
PERMISSIBLEMATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPERCONSISTSOF 6 PAGES{Including this front page)
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SECTION A
QUESTION 1 (22 marks)
Write down the letter corresponding to your choice next to the question number.
= 1.1 A random sample of size n 11 was selected from a population and the data are as
follows: 32,30, 45, 23, 51, 82 ,69, 12 ,71,65, 42. Use this dataset to answer questions
1.1.1 through 1.1.3
1.1.1 The point estimate for the mean is
[2]
A. 50.5
B. 47.45
C.
32
D.
45.47
1.1.2 The point estimate for the standard deviation
[2]
A. 22.29
B. 29.22
C. 496.67
D.
67
1.1.3 The standard error of the sample mean is equal to
[2]
A.
50.3
B. 6.72
C. 71.6
D. 22.29
1.2 Which of the following is a property of the median
[2]
A.
there may be no median
B. there may be several medians
C.
not affected by extreme values
D. not unique
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= = 1.3 Which of the following test can be used in statistics when n 30 and (J 5 ? [2]
A.
T-test
B. Z-test
C. one-way ANOVA
D. Kruskal-Wallis test
1.4 Inferential statistics are techniques that allow us to use:
[2]
A.
samples to make generalizations about the populations from which the
samples were drawn
B.
population parameter to make generalizations about the whole populations
C.
population parameter to make generalizations about the sample statistics
D. calculate sample statistics
1.5 As part of a study to investigate the effects of stubble burning, one of the variable
measured at the site is type of crop grown (e.g.,0=maize,l= oats, 2= others). [2]
Which measurement scale should be considered when analysing this variable
A. ordinal
B. interval
C. nominal
D. ratio
1.6 The sampling technique whereby members of the population are placed in an array
and every tenth member is selected is an example of:
[2]
A.
Random sampling
B. Systematic sampling
C. Cluster sampling
D. Stratified sampling
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1.7 The variable number of goats born per year is a____
random variable
[2]
A.
continuous
B.
descriptive
C.
discrete
D.
normal
1.8 Which of the following is a condition for binomial distribution
[2]
A.
The probability of success does not change from trial to trial
B.
Trials are dependent
C.
more than two outcomes are expected
D
P + q >1
1.9 The average number of goats sold by the Phalao farm is 5 goats per day. What is the
probability that exactly 3 goats will be sold tomorrow?
[2]
A. 0.1404
B. 0.2123
C.
0.8422
D. 0.2807
SECTION B (Clearly show all your work)
QUESTION 2 [41 marks]
2.1 In 2015, three hundred deaths of cows related to drought were recorded daily in
Omusati region. The table below display the grouped data for three hundred cows
that died because of drought just within 40 days.
Days
0-5 5-10 10-15 15-20 20-25 25-30 30-40
Number of cows
2
0
8
36
110 78
66
2.1.1 Estimate the mean, median and the mode of the distribution.
[10]
2.1.2 Find the variance and the standard deviation for the dataset.
[5]
4
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2.1.3 Suppose that you suspected an outlier in the dataset above, which measure of
central location would you prefer to describe the data and why?
[2]
2.2 Let X be the random variable with the following probability distribution
I:(XI I:as I:.3 I:.25 I:2s I~1s
2.2.1 Estimate the mean for a random variable 2X
[4]
2.2.2 Estimate the variance and the standard deviation for a random variable X
[S]
2.2.3 Find P(X 2)
[2]
2.3 In a citrus orchard it is found that 5% of the oranges are affected by a disease. To
test for the presence of the disease a farmer selects six trees at random. If Xis a
binomial random variable which represent the number of trees affected:
NB round your answers to 4 d.p
2.3.1 What is the probability that exactly two trees are affected
[3]
2.3.2 What is the probability that at most one tree is affected
[4]
2.3.3 What is the probability that more than five trees are affected
[2]
2.3.4 Calculate the mean and variance for the random variable X
[4]
QUESTION 3 [26 marks]
3.1 Consider a machine which is filling bottles with milk at Namib diaries. Experience has
shown that in this process the population of fill volume are normally distributed with
a standard deviation of 1.35 ml. The manager wants to collect a sample just large
enough to provide a sample mean within 0.50 ml of the true process mean at the 90%
confidence level. Calculate the sample size needed
[3]
3.2 A dairy processing company claims that the variance of the amount of protein in the
whole milk processed by the company is more than 0.3 mg. You suspect that this is
wrong and find that a random sample of 25 milk containers has a variance of 0.27.
At 1% level of significance, is there enough evidence to reject the company's claim?
3.2.1 State the hypothesis that you would use to test the company's claim.
[2]
3.2.2 Test the hypothesis in question 3.2.1
[7]
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3.2.3 Construct a 95% confidence interval for the unknown population standard deviation
[5]
3.3 Tangi grows maize in her two small plots of equal sizes. She is interested in
comparing the mean yields from two plots after applying fertilizer A and B to the two
plots respectively. She monitors the yields (in 100kg) for period five consecutive
years. The table below shows the results recorded:
2012
2013
2014
2015
2016
Fertilizer A 7.4
5.2
6
4.3
8.3
Fertilizer B 5.5
5
3.5
4.5
7
Estimate the mean difference between the maize yields for Julia's plots, using a 99%
confidence level.
[9]
QUESTION 4 (11 marks]
4.1 The table below shows the heights (in meters) of a random sample of eight guava
trees in Haingura's backyard garden.
Tree
A
B
C
D
E
F
G
H
Height 1.05
0.99
1.2
1.36 1.55 0.98
0.95
0.85
4.1.1 Estimate the variance of the entire population of guava trees in Haingura's garden
with a 95% degree of confidence.
[9]
4.1.2 Haingura decides to continue growing guava trees in his garden if the population
variance for the height of these trees is more than 1.55 meters. Formulate the null
and alternative hypothesis that he would use if he wished to test for the above
claim.
[2]
END OF EXAMINATION QUESTIONPAPER
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FORMULASHEET
= Me + L c[O.Sn-CF]
fme
x-=- "f.fx
n
tstat
=
x-µ
-s-
.,/n
2 _ (n-1)5 2
Xstat - uz
E(X) = L.XiPi
P(X = x) = (;) pxqn-x
= b n"f.xy-"f.x"f.y
n"f.x2-("f.x) 2
J[=-1 X __+X 2
n1+nz
x- =-
"f.x
n
p±zf!
Z
=
x-µ
-cr-
../n
2 _ "(fo-fe) 2
Xstat - L, fe
a= y- bx
s 2 =;c"fc.(_x·"-x-)-2'-
n-1
= s2 "f.(x;-x)z f;
n-1
P(X = k) = e-eex
x!
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TABLE of CRITICAL VALUES for STUDENT'S t DISTRIBUTIONS
Column headings denote probabilities (a) above tabulated values.
d.f. 0.40 0.25
1 0.325 1.000
2 0.289 0.816
3 0.277 0.765
4 0.271 0.741
5 0.267 0.727
6 0.265 0.718
7 0.263 0.711
8 0.262 0.706
9 0.261 0.703
10 0.260 0.700
11 0.260 0.697
12 0.259 0.695
13 0.259 0.694
14 0.258 0.692
15 0.258 0.691
16 0.258 0.690
17 0.257 0.689
18 0.257 0.688
19 0.257 0.688
20 0.257 0.687
21 0.257 0.686
22 0.256 0.686
23 0.256 0.685
24 0.256 0.685
25 0.256 0.684
26 0.256 0.684
27 0.256 0.684
28 0.256 0.683
29 0.256 0.683
30 0.256 0.683
31 0.256- 0.682
32 0.255 0.682
33 0.255 0.682
34 0.255 0.682
35 0.255 0.682
36 0.255 0.681
37 0.255 0.681
38 0.255 0.681
39 0.255 0.681
40 0.255 0.681
60 0.254 0.679
80 0.254 0.678
100 0.254 0.677
120 0.254 0.677
140 0.254 0.676
160 0.254 0.676
180 0.254 0.676
200 0.254 0.676
250 0.254 0.675
inf 0.253 0.674
0.10
3.078
1.886
1.638
1.533
1.476
1.440
1.415
1'.397
1.383
1.372
1.363
1.356
1.350
1.345
1.341
1.337
1.333
1.330
1.328
1.325
1.323
1.321
1.319
1.318
1.316
1.315
1.314
1.313
1.311
1.310
1.309
1.309
1.308
1.307
1.306
1.306
1.305
1.304
1.304
1.303
1.296
1.292
1.290
1.289
1.288
1.287
1.286
1.286
1.285
1.282
0.05
6.314
2.920
2.353
2.132
2.015
1.943
1.895
1.860
1.833
1.812
1.796
1.782
1.771
1.761
1.753
1.746
1.740
1.734
1.729
1.725
1.721
1.717
1.714
1.711
1.708
1.706
1.703
1.701
1.699
1.697
1.696
1.694
1.692
1.691
1.690
1.688
1.687
1.686
1.685
1.684
1.671
1.664
1.660
1.658
1.656
1.654
1.653
1.653
1.651
1.645
0.04
7.916
3.320
2.605
2.333
2.191
2.104
2.046
2.004
1.973
1.948
1.928
1.912
1.899
1.887
1.878
1.869
1.862
1.855
1.850
1.844
1.840
1.835
1.832
1.828
1.825
1.822
1.819
1.817
1.814
1.812
1.810
1.808
1.806
1.805
1.803
1.802
1.800
1.799
1.798
1.796
1.781
1.773
1.769
1.766
1.763
1.762
1.761
1.760
1.758
1.751
0.025
12.706
4.303
3.182
2.776
2.571
2.447
2.365
2.306
2.262
2.228
2.201
2.179
2.160
2.145
2.131
2.120
2.110
2.101
2.093
2.086
2.080
2.074
2.069
2.064
2.060
2.056
2.052
2.048
2.045
2.042
2.040
2.037
2.035
2.032
2.030
2.028
2.026
2.024
2.023
2.021
2.000
1.990
1.984
1.980
1.977
1.975
1.973
1.972
1.969
1.960
0.02
15.894
4.849
3.482
2.999
2.757
2.612
2.517
2.449
2.398
2.359
2.328
2.303
2.282
2.264
2.249
2.235
2.224
2.214
2.205
2.197
2.189
2.183
2.177
2.172
2.167
2.162
2.158
2.154
2.150
2.147
2.144
2.141
2.138
2.136
2.133
2.131
2.129
2.127
2.125
2.123
2.099
2.088
2.081
2.076
2.073
2.071
2.069
2.067
2.065
2.054
0.01
31.821
6.965
4.541
3.747
3.365
3.143
2.998
2.896
2.821
2.764
2.718
2.681
2.650
2.624
2.602
2.583
2.567
2.552
2.539
2.528
2.518
2.508
2.500
2.492
2.485
2.479
2.473
2.467
2.462
2.457
2.453
2.449
2.445
2.441
2.438
2.434
2.431
2.429
2.426
2.423
2.390
2.374
2.364
2.358
2.353
2.350
2.347
2.345
2.341
2.326
0.005
63.656
9.925
5.841
4.604
4.032
3.707
3.499
3.355
3.250
3.169
3.106
3.055
3.012
2.977
2.947
2.921
2.898
2.878
2.861
2.845
2.831
2.819
2.807
2.797
2.787
2.779
2.771
2.763
2.756
2.750
2.744
2.738
2.733
2.728
2.724
2.719
2.715
2.712
2.708
2.704
2.660
2.639
2:626
2.617
2.611
2.607
2.603
2.601
2.596
2.576
0.0025 0.001 0.0005
127.321 318.289 636.578
14.089 22.328 31.600
7.453 10.214 12.924
5.598 7.173 8.610
4.773 5.894 6.869
4.317 5.208 5.959
4.029 4.785 5.408
3.833 4.501 5.041
3.690 4.297 4.781
3.581 4.144 4.587
3.497 4.025 4.437
3.428 3.930 4.318
3.372 3.852 4.221
3.326 3.787 4.140
3.286 3.733 4.073
3.252 3.686 4.015
3.222 3.646 3.965
3.197 3.610 3.922
3.174 3.579 3.883
3.153 3.552 3.850
3.135 3.527 3.819
3.119 3.505 3.792
3.104 3.485 3.768
3.091 3.467 3.745
3.078 3.450 3.725
3.067 3.435 3.707
3.057 3.421 3.689
3.047 3.408 3.674
3.038 3.396 3.660
3.030 3.385 3.646
3.022 3.375 3.633
3.015 3.365 3.622
3.008 3.356 3.611
3.002 3.348 3.601
2.996 3.340 3.591
2.990 3.333 3.582
2.985 3.326 3.574
2.980 3.319 3.566
2.976 3.313 3.558
2.971 3.307 3.551
2.915 3.232 3.460
2.887 3.195 3.416
2.871 3.174 3.390
2.860 3.160 3.373
2.852 3.149 3.361
2.847 3.142 3.352
2.842 3.136 3.345
2.838 3.131 3.340
2.832 3.123 3.330
2.807 3.090 3.290
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Z-Table
The table shows cumulative probabilities for the standard normal curve.
Cumulative probabilities for NEGATIVE z-values are shown first. SCROLL
DOWNto the 2nd page for POSITIVEz
z
-3.4
-3.3
-3.2
-3.1
-3.0
-2.9
; -2.8
-2.7
-2.6
-2.5
-2.4
-2.3
-2.2
-2.1
-. 2.0
-1.9
-1.8
-1.7
-1.6
-1.5
-1.4
-1.3
-1.2
-1.1
-1.0
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
I -0.3
-0.2
-0.1
0.0
.00
.0003
.0005
.0007
.0010
.00'!3
.0019
.0026
.0035
.0047
.0062
.0082
.0"!07
.0139
.0179
.0228
.0287
.0359
.0446
.0548
.0668
.0808
.0968
.1151
.1357
.-1587
.1841
.21'19
.2420
.2743
.3085
.3446
.3821
.4207
.4602
.5000
.01
.0003
.0005
.0007
.0009
.0013
.0018
.0025
.0034
.004~,
.0060
.0080
.0'104
.0136
.0174
.0222
.028"1
.0351
.0436
.0537
.0655
.0793
.0951
.1'13'1
.1335
.1562
.'1814
.2090
.2389
.2709
.3050
.3409
.3783
.4168
.4562
.4960
.02
.0003
.0005
.0006
.0009
.0013
.00"18
.0024
.0033
.0044
.0059
.0078
0-102
.0'132
.0170
.0217
.0274
.0344
.0427
.0526
.0643
.0778
.0934
.-1112
."IJ14
.'!539
.1788
.206"1
.2358
.2676
.10·15
.3372
.3745
.4'129
.4522
.4920
.03
.0003
.0004
.0006
.0009
.0012
.0017
.0023
.0032
.0043
.0057
.0075
.0099
0129
.0166
.0212
.0268
.0336
.04'18
.05'16
.0630
.0764
.09'18
.1093
.1292
:1515
.'1762
.2033
.2327
.2643
.2981
.3336
.3707
.4090
.4483
.4880
.04
.0003
_00,:)4
.0005
.0008
.0012
.00'16
.0023
.003'1
.004"1·'.
.0055
.0073
.0096
.0125
.0162
.0207
.0262
.0329
.0409
.0505
.0618
.0749
_09{)'1
.1075
.1271
.1492
.1736
.2005
.2296
.2611
.2946
.3300
.3669
.4052
.4443
.4840
.05
.0003
.0004
.0006
.0008
.0011
.0016
.0022
.0030
.0040
.0054
.007'I
.0094
.0122
.0158
.0202
.0256
.0322
.0401
.0495
.0606
.0735
.0885
. 1056
.1251
. 1469
.1711
.1977
.2266
.2578
.29;12
.3264
.3632
.4013
.4404
.4801
.06
.0003
.0004
.0006
.0008
.00-1-1
.0015
.002'1
,0029
.0039
.0052
.0069
.009-1
.0119
.0'154
.0·197
.0250
.0314
.0392
.0485
.0594
.0721
.0869
.1038
.1230
.1446
.1685
.'1949
.2236
.2546
.2877
.3228
.3594
.3974
.4364
.4761
.07
.0003
.0004
.0005
.0008
.0011
.00'15
.0021
.0028
.0038
.005·1
.0068
.0089
.0116
.0150
.0192
.0244
.0307
.0384
.0475
.0582
.0708
.0853
.1020
.1210
.1423
.'1660
.'1922
.2206
.2514
.2843
.3192
.3557
.3936
.4325
.4721
.08
.09
.0003 .0002
.0004 .0003
.0005 .0005
.0007 .0007
.OO"IO .0010
.0014 .00'14
.0020 .0019
.0027 .0026
.0037 .0036
.0049 .0043
.0066 .0064
.0087 .0084
.0113 .0'1"10
.0146
.0188
.0239
-
.0233
_030·1 .0294
.0375 .0367
.0465 .0455,
.0571 .0559
.0694 .0681
.0838 .0823
.'1003 .0985
.1·190 .1170
.'1401 .1379
.1635 .161'I
.1894 ."1867
.2177 .2"148
.2483 .2451
.2810 .2776
.3"156 .3121
.3520 .3483
.3897 .3859
.4286 .4247
.4681 .464'1
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1.10 Page 10 |
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Cumulative probabilities for POSITIVE z-values are shown below .
z
.00
.01
0.0
.5000 .5040
0.1
.5398 .5438
0.2
.5793 .5832
0.3
.6179 .6217
I 0.4
l 0.5
.6554 .6591
.6915 .6950
0.6
.7257 .7291
0.7
.7580 .76'1'1
0.8
.7881 .7910
0.9
.8159 .8186
1.0
.84"13 .8438
1.1
.8643 .8665
1.2
.8849 .8869
1.3
.9032 .9049
1.4
.9192 .9207
1.5
.9332 .9345
1.6
.9452 .9463
1.7
.9554 .9564
.I I i 1.8
.9641 .9649
' 1.9
2.0
.97"13 .97'19
.9772 .9778
2.1
.9821 .9826
2.2
.986'1 .9864
2.3
.9893 .9896
2.4
.99'18.. .9920
2.5
.9938 .9940
2.6
.9953 .9955
; 2.7
.9965 .9966
2.8
.9974 .9975
2.9
.9981 .9982
3.0
.9987 .9987
3.1
.9990 .999'1
J.2
.9993 .9993
3.3
.9995 .9995
3.4
.9997 .9997
.02
.5080
.5478
.587'1
.6255
.6628
.6985
.7324
.7642
.7939
.8212
.8461
.8686
.8888
.9066
.9222
.9357
.9474
.9573
.9656
.9726
.9783
.9830
.9868
.9898
.9922
.9941
.9956
.9967
.9976
.9982
.9987
.9991
.9994
.9995
.9997
.03
.5120
.5517
.5910
.6293
.6664
.7019
.7357
.7673
.7967
.8238
.8485
.8708
.8907
.9082
.9236
.9370
.9484
.9582
.9664
.9732
.9788
.9834
.9871
.9901
.9925
.9943
.9957
.9968
.9977
.9983
.9988
.9991
.9994
.9996
.9997
.04
.5160
.5557
.5948
.633'1
.6700
.7054
.7389
.7704
.7995
.8264
.8508
.8729
.8925
.9099
.925'1
.9382
.9495
.9591
.9671
.9738
.9793
.9838
.9875
.9904
.9927
.9945
.9959
.9969
.9977
.9984
.9988
.9992
.9994
.9996
.9997
.05
_5-199
.5596
.5987
.6368
.6736
.7088
.7422
.7734
.8023
.8289
.8531
.8749
.8944
.91'15
.9265
.9394
.9505
.9599
.9678
.9744
.9798
.9842
.9878
.9906
.9929
.9946
.9960
.9970
.9978
.9984
.9989
.9992
.9994
.9996
.9997
.06
.5239
.56.36
.6026
.6406
.6772
.7123
.7454
.7764
.805'1
.8315
.8554
.8770
.8962
.9131
.9279
.9'106
.95i5
.9608
.9686
.9750
.9803
.9846
.9881
.9909
.9931
.9948
.9961
.9971
.9979
.9985
.9989
.9992
.9994
.9996
.9997
.07
.5279
.5675
.6064
.6443
.6308
.7157
.7486
.7794
.8078
.8340
.8577
.8790
.3980
.9147
.9292
.9418
.9525
.96'16
.9693
.9756
.9808
.9850
.9884
.9911
.9932
.9949
.9962
.9972
.9979
.9985
.9989
.9992
.9995
.9996
.9997
.08
.5319
.57·14
.6"103
.6480
.6844
.7"190
.7517
.7823
.8'106
.8365
.8599
.8810
.8997
.9162
.9306
.9429
.9535
.9625
.9699
.9761
.98·12
.9854
.9887
.9913
.9934
.9951
.9963
.9973
.9980
.9986
.9990
.9993
.9995
.9996
.9997
.09
.5359
.5753
.6'14'1
.6517
.6879
.7224
.7549
.7852
.8133
.8389
.862'1
.8,S30
.9015
.9'177
.93'19
.9441
.9545
.9633
.9706
.9767
.98'17
.9857
.9890
.99'16
.9936
.9952
.9964
.9974
.99£1"1
.9986
.9990
.9993
.9995
.9997
.9998
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2 Pages 11-20 |
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2.1 Page 11 |
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APPENDIX E: The Chi-Square Distribution
..
:··.· ·x~·._, . ,;
I
i I i I i ! i ldl\\p .995
.990
.975
l l .950
.9~~ ·, .750 ;--~00
.250
.100 : .050
.025
!1J0.00004 fo.00016 fo.ooo9s :0.00393 f{J.o1s19 [0.10153 [0.45494 11.32330 jl.70554 IJ.84146 1s.om9 ~j1.s1944
!
2 ~fo.02010
lo.o5o64 _io.10259 _!o.2w12 jo.575J6 _ ~38629 !2.77259_1460511 _!s.99146 ·[urr/6~110.596631
! fJ 0.01112 fo.ii483 10.21580 fo.35185 ·fo.58437 [°imsJ j2.36597 /4.10834 f6.2s139 ?-81473 19.34840 I 11.344s1 fii:'.s3816·!
i i i 4 10.20699 10.29711 0.48442 0.71072 r1.06362 ~2256 !J.35669 rs.38527 , 7.77944 19.48773 1I 1.14329 ~70
114-860261
! f i i I I !5jo.41174 fo.55430 lo.83121 p.14548 1.61031 Jz.67460 '4.35146 6.62568 j9.23636 '11.01oso 12.83250 15.08627 16.74960
i i l 6 /0.67573 ro.87209 : 1.23734 fi.63538 12.20413 f3.45460 ,5.34812 l 7.84080 10.64464 !12.59159 !14.~938 l6.81189118.54758
r 16 i i i : -7 -i 0.98926·-11.·2J904 ; 1.68987- 2.16735--rz.83311-,4.25485 - .34581 ; 9.03715. 12.01704 rl4.06714 16.01276 18.4;53I ;~~-27774
! f I ·j I [- s·•·1··.3j4441 [l.646so (2.11913·• [2.73264.. 3.48954·· 5.01064 7.34412 10.21885 !1J.36157/ 15.50131 f11.s3455 _i20.o<Jo24 21.954;5
I l l 9 jU3493 12.08790 ;2~70039 13.32511 14.16816 /5.89883 jS.3428] j 11.38875 14.68366 16.91898j19.0m7J21.66599123.58935_
r 1 10.. ,2.15586 ·-, 2.55821···13.24697--, 3.94030 ·14.86518--16.73720-·19.34182 ·: 12.54886115.98718 ; 18.30704.120.48318 23.20925 j25.18818
! !11!2.60J22 ·JJ.05348 ~i4.574s1
l5.5ms i1.58414 J10_34100[_13.10069fl1.21501 19.61s14 f21.92oos-J24.12491 l2G.1s6s5
i1"i· 1B:S:ii:isfi.i":oi601·:ii"3366<>-l i:i:011iu-'1is-iiis'i.
t.
(
! ~! i i i ~I 13 j3.56503
! f:i".-:iii'ii;jT522601
!
I
~
. •1.6-:3ois0TsI-::i3s42
1u4on
I
i
I
M.84540
1
1
.
'
t
26.21691 j·'i"s:299.52.
S.00875 5.89186 p.04150 19.29907 jl2.33976 15.98391 \\ 19.81193 22.36203 J24.73560
29.81947'
I ! flo.i6S:llTlm21jl?:11;;;;;- I i-i.·.·14.07467 4.66043 5.62873 J6.57063-;7:-;8953
fii.06414-J23.68479 / 26. l 1895 29.14124 fli31935:
fl's[ r f I ! I f f I ! i 4.60092 5.22935 6.26214 j 7.26094 8.54676 I 1.036S4·114.33886 18.24509 22.30713 24.99579 27.48839 30.57791 32.80132
! 116/s.14221
j5.69ilIl ! ! i : 11
j5.s1221 16.90766 !7,96165 J9.3l224 j11.91222 115.33850 19.36886J23.54183 !26.29623 [2s.84535!3L9~99313~:26719
6.40776 1.s6419 x.67176 110.os519 )12.79193 16.33818 120.48868: 24.769o4121.ss111 fJo.19101 f33.40866135.11847
Gs! I ! ! ! ! i 6.26480 7.01491 8.23075 _,9.39046 I0.86494113.67529 17.33790 21.60489 (25.98942 28.86930 ~j34.80531137.15645
I r i ! !.19 16.84397 j'l.63273 8.90652 Go.11101.' 11.65091 14.56200 j 18.33765 22.71781 fi.1.20357 J 30.14353 32.85233·J36.19087138.58226 I
i 1 20 17.43384 18.26040 19.59078 jl0.85081 12.44261 115.45177r19.33743: 23.82769 128.41198 :31.41043.134.16961 137.56623 139.996851
I j ! jl3.23%0! 21 j8.03365. js.s9120 10.28290 11.59131
! 16.34438!20.33723 i24.9347H j29.61so<1J~2.61os1 !3SA7888 jJS.93211 F40106
I I i I I ! ~! i 22 fs.64272 9.S4249 11l.98232 12.33801 l4.04149 j17.23962 21.33704 26.03927 ; 30.81328
i I 36.78071 40.28936 42.795651
i 1 i , 23 r9.26042 110.19572 , I l.6.~855113.09051 14.84796 118.13730122.33688i 27.14134 32.00690 : 35.17246 38.07563 141.63840144.18128
1241 1 1 r r 1 1 9.88623 J0.85636 112.40115 113.84843__15.65868 19.03725 23.33673 128.24115 133.19624 j36.4l503 39.3r.408 42.97982:145.55851
rzs 1 1 r 12 7 14 \\I0.51965 111.52398 13.11972 14.61141 116.47341 19.93934 4.33659 : 29.3~885:134.38159 13 .6~24~ 140.64647 4.31410J46.92789
r j j26JW6024:!'2'9_815
j n.84390 [ 1~.37916!11.291s8120.84343 25.33646 j3Q.43457_!35.5631713s.88514 l41.9231: 14s.~16s [\\s.28988
1 27 11.80759_112.87850 114.57338 116.15140·: I8.11390 121.74940126.33634 31.5284I 136.74122 :40.11327 143.19451 146.96294 149.644921
~~4'~~-30786
iIG.92788 j18.93924_jll.6S7l6 !.27.33623~!37.91592
~3714f44.46079148.27824_~!,
I i ! I j 29 IJ.1211s j 14.25645 j 16.04707 17.70837 19.76774 j23.566S9 j2B.33613 !33.71091 [39.oS747 J42.55697 j4s.12229!49.58788152.33562
i fw.mi} ! 30 /13.78672·114.95346116.79077 rl8.49266
j24.47761 29.33603 !34.79974/40.25602 143._77297i46.97924·jso.89218153.67196
Page7 of7