 |
BBS112S - BASIC BUSINESS STATISTICS 1B - 2ND OPP - JANUARY 2024 |
|
|
1 Page 1 |
▲back to top |
nAml BIA UntVERSITY
OF SCIEnCEAnDTECHnOLOGY
FacultyofHealthN, atural
ResourceasndApplied
Sciences
SchoolofNaturaland Applied
Sciences
Departmenot fMathematics.
StatisticsandActuariaSl cience
13JacksonKaujeuaStreet
PrivateBag13368
Windhoek
NAMIBIA
T: •264 61207 2913
E: msas@nust.na
W: wv.w.nust.na
QUALIFICATION: B. Business Ad min, B. Marketing, B. Human Resource Management, B.
Public Management and B. Logistics and Supply Chain Management
QUALIFICATIONCODE: 21BBAD / 07BMAR / 07BHR /
24BPN / 07BLSM
COURSE:BASIC BUSINESS STATISTICS lB
DATE: JANUARY 2024
DURATION: 3 HOURS
LEVEL:6
COURSECODE: BBS112S
SESSION: 1
MARKS: 100
SUPPLEMENTARY/SECOND OPPORTUNITY: EXAMINATION QUESTION PAPER
EXAMINERS: MR E. MWAHI,MRS. KASHIHALWAM, RJ. AMUNYELAD, R.J. MWANYEKANGE,
MRS A. SAKARIAM, S. N. PONHOYOMWENEM, RS L. KHOA
MODERATOR: MR J. SWARTZ
INSTRUCTIONS:
1. Answer all questions on the separate answer sheet.
2. Please write neatly and legibly.
3. Do not use the left side margin of the exam paper. This must be allowed for the examiner.
4. No books, notes and other additional aids are allowed.
5. Mark all answers clearly with their respective question numbers.
PERMISSIBLE MATERIALS:
1. Non-Programmable Calculator
ATTACHEMENTS:
1. T- Table
2. Normal distribution table
3. Chi-square table
This paper consists of 6 pages including this front page.
|
|
2 Page 2 |
▲back to top |
-----
QUESTION1
[20 MARKS]
1.1 If true value of population parameter is 10 and estimated value of population
parameter is 15 then error of estimation is:
[2]
A. 5
B.25
C. 1.5
D. 0.667
1.2 A random sample of 100 observations is to be drawn from a population with a mean
of 40 and a standard deviation of 25. The probability that the mean of the sample
will exceed 45 is.
[2]
A. 0.477
B. 0.4207
C. 0.0793
D. 0.0228
1.3 Suppose we sample by selecting every fifth invoice in a file after randomly obtaining
a starting point. What type of sampling is this?
[2]
A. Simple random sampling.
B. Cluster random sampling.
C. Stratifies random sampling.
D. Systematic random sampling.
1.4 A 95% confidence interval for a population mean is determined to be 100 to 120. If
the confidence level is reduced to 90%, the interval:
[2]
A. Becomes narrower.
B. Becomes wider.
C. Does not change.
D. Becomes 0.1.
1.5 An interval estimate is a range of values used to estimate:
[2]
A. The shape of the population's distribution.
B. The sampling distribution.
C. A sample statistic.
D. A population parameter.
BASICBUSINESSSTATISTICS18 (B)
2NDOpportunity January 2024
2
|
|
3 Page 3 |
▲back to top |
1.6 Suppose that we wanted to estimate the true average number of eggs a queen bee
lays with 95% confidence. The margin of error we are willing to accept is 0.5. Suppose
we also know that the population standard deviation is 10. What sample size should
we use?
[2)
A.1536
B.1537
C.2653
D.2650
1.7 Which of the following is true of the null and alternative hypotheses?
(2)
A. Exactly one hypothesis must be true.
B. both hypotheses must be true.
C. It is possible for both hypotheses to be true.
D. It is possible for neither hypothesis to be true.
1.8 A type II error occurs when:
(2)
A. the null hypothesis is incorrectly accepted when it is false.
B. the null hypothesis is incorrectly rejected when it is true.
C. the sample mean differs from the population mean.
D. the test is biased.
1.9 Test of hypothesis Ho: µ = 50 against Hl: µ > 50 leads to:
(2)
A. Left-tailed test
B. Right-tailed test
C. Two-tailed test
D. Difficult to tell.
1.10 Which hypothesis is always in an inequality form?
(2)
A. Null hypothesis
B. Alternative hypothesis
C. Simple hypothesis
D. Composite hypothesis
BASIC BUSINESSSTATISTICS18 (B)
2NDOpportunity January 2024
3
|
|
4 Page 4 |
▲back to top |
QUESTION 2
[23 MARKS]
2.1 Mention four reasons why we take samples instead of enumerating whole
populations.
[4]
2.2 Suppose that the mean intelligence of 1800 high schoolboys is known to be normally
distributed with a mean of 200 and a standard deviation of 16. A sample of 36 is
drawn from this population.
2.2.1 How many schoolboys have the mean intelligence of more than 195? [4]
2.2.2 What is the probability that the mean of this sample is between 193
and 207?
[5]
2.3 Statistics students believe that the mean score on the first statistics test is 66.5. Their
lecturers think this is not true. They sampled ten statistics students and obtains the
following scores below. The data are from a normal distribution.
65; 65; 70; 67; 66; 63; 63; 68; 72; 71
Using the scores above, test the students' claim using a 1% level of significance. [10]
QUESTION 3
(23 MARKS]
3.1 The time to repair an electronic instrument at Paco Engineering is a normally
distributed random variable measured in hours. The repair times for 16 such
instruments chosen at random are as follows:
159
280
101
212
224
379
179
264
222
362
168
250
149
260
485
170
3.1.1 Find the sample variance of these data
[3]
3.1.2 Estimate the population variance of time to repair electronic instruments at
this film. Use the 90% level of confidence.
[10]
BASICBUSINESSSTATISTICS18 (B)
2N°Opportunity January 2024
4
|
|
5 Page 5 |
▲back to top |
-------
3.2 The table below shows data on type of school area and the students' choice of good
grades, athletic ability, or popularity as most important.
Goals
Good grades
Athletic ability
Popularity
Urban
24
6
5
Type of school area
Suburban
87
42
22
Rural
57
50
42
At the 5% level of significance, is there a relationship between the type of school
area and the students' choice of good grades, athletic ability, or popularity as most
important?
[10]
QUESTION 4
[34 Marks]
4.1 The table shows Emma's spelling test scores from January to December 2016.
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
5
6
6
6
7
6
6
7
5
7
6
7
4.1.1 Compute a centred 2-period moving average scores for Emma's spelling test scores.[7]
4.1.2 Compute the estimated straight line trend equation by the method of least squares
using the sequential coding method, start the coding from 0.
[10]
4.1.3 Estimate when Emma's spelling test score is expected to be equals to 8.
[5]
4.2 The following are prices and consumption quantities for three commodities in 1995
and 2002.
Commodity
A
B
C
Price
2
10
3
1995
Quantity
20
3
15
Price
3
40
4
2002
Quantity
20
2
20
Using 1995 as the base year, calculate and interpret the following:
4.2.1 The price relative for commodity C
[2]
BASICBUSINESSSTATISTICSlB (B)
2N°Opportunity January 2024
5
|
|
6 Page 6 |
▲back to top |
4.2.2 The aggregate quantity index
[4]
4.2.3 The Paascheweighted aggregate price index
[6]
=============END OF EXAMINATION===========
BASICBUSINESSSTATISTICSlB (B)
2N°opportunity January 2024
6
|
|
7 Page 7 |
▲back to top |
e.g.. for.: = - l.34. refer to the - 1.3
row o.ndthe 0.04 column to
r- tiod the cumulotivc orco,0.0901.
The Standard Normal Distribution
0
z
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010
-2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014
-2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019
-2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026
-2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036
-2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048
-2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064
-2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084
-2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110
-2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143
-2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183
-1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233
®
-1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294
-1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367
-1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455
-1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559
-1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681
-1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823
-1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985
-1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170
-1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379
-0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611
-0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867
-0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148
-0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451
-0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776
-0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121
-0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483
-0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859
-0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247
-0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641
Source:Cumulativestandardnormalprobabilitiesgeneratedby M1nitabt.hen roundedto four decimalplaces.
5217X_JBC.lndd 1
I 04/02/10 8:53 PM
|
|
8 Page 8 |
▲back to top |
e.g .. for~ = 1.34, refer to the
1.3row and the 0.04 column to
fwd the cumulative :ir~a. 0.9099.
TheStandardNormal Distribution
0
z
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517
0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879
0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852
0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133
0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621
@)
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633
1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767
2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817
2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857
2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890
2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964
2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974
2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990
I 5217X_IBC.lndd 2
I 04/02/10 8:53 PM
|
|
9 Page 9 |
▲back to top |
APPENDIX D: The t-distribution
r··- J 1
·
d~p ···--~·~_?
?-2~~l-_. 0.10
-r 0.05
!ie..Q!:'
[ . 0.025 _ .. . o.oi~-
"······-····-··········
OJJOS-~~-<-l00O5
__ I_
2
~-3 _
[_ 4
····-==-=·····' ~:??.?..?)~?__:0O77_684 I 6.313752 .....112.70620 31.82052 [163.65674 ___,, 636.6192.
0.288675o.8164971.8856182.91998··61·~.3026?6.96456I[9.92484f31.5991
o.27-66701.7648921.6377442.3533·6···31···3.182454.5407015.84091:12.9240
0.270722o.74069711.5332062.131847l?:776._45..~-7~69_5I4.60409 18.6103
5
6
0.26?181,o7. 26687:1:.-4~7-588j42.0150.4:~8l~:5-??_._?~:3.~~.-~1i14:0321.4[s.:8688_
· o.2.648·315.0.717_5_:5·i8;~~975J61,9431··3·01··~·;·~~·9·1··i·i·d·26?·.·.·J·i~:.7?74···31.5.~_?_88
.-.···-?...-·.-?.:~_?3.~0~.771114j 2x:i1.~..,9.1..8~.9.~.45.7J.9z_.3646..2...2. .997..9..J5 3.4994815.4079
-···-s o·:261s2,oi :·;.ci'sil8i~73968i·s L8595·4·812:305··0·0··2·.·8·9· 6461i3s53·9· 15.0413
9 .?-~~?.~..~_??..:?.?~.?.1-~,3~8302..9{·.8331~[32.262.16:2.8214413.249·8··4-i4.78o9
-.-..-.-.~..-.~-.?.:.~...~..?.?...-~80.699812~:jf?.1....8. 41.8124.61[i.2. ~ii.: ..127.637.7·1ii:6927.-. 4.5869
_.._...~. ~...0...25955·-60' .6974.4..5.ri:3634301.79588·51~-~?...?..!9.2.9.7.1808·13.1058..1.:-4.437.0...._..
12 0.2590.3..3.·.?::~9.~··i:~rj1:3562.:.·.ii.:-:,i;8-"z:2a1s2.:·1:7.:8811'2.68·1··0·]0·3·.·0··5·4.5.·4...4....3. 178.
13 0.25859·1·o.6938219.35017..1i.7709·33'f:i.16?.37
I3.01228 4.220·8··
-··14.. 0.2582130.692417'1~3450310.76131..0.2..:.144.79. 12.6..2449 2.976_8_4_..4:1'4.0...5.....
L._1~ . 0.2578850.6~;~~;[i.34060-6~~;5;~51~2._131.4. 5l~:??..2..48J2~946-7.1.:.~;?.?.-.~.~~::::
L_._16 .. ?:~?.??~~o-:·-6··901312L3367517.7458·8_412.u991·.12.583·4_912.920·78.i~§.~5-0~·=
17 0.257347o.68919l5~:~~3~?91.:7396072.10932lz.5669· ·312.898233.9651
1
1s 0.257123o.68836141~:3.3.?3.1.~.7~3-4·-0-6--4~:1009· 2:]2.::5~2.:.~::~1:2-.·:aia414~·3-_92_1-::-6==
---~--· o:2·s692o3.68762·11u·2··772a··1·:·7·29.1..3.·.31·.·2.09302[2:s-3.9..4.·812:860··9·3 3.883··4.._...
--;210 ..... ___ o.686352
··1.-72··-4·7·-·1·182··-:··o··a··5···9····6-·:··2;···::·-s;2{;7~9;··8·-r1i2a:ia·415;~·3..·'4··'·1·3· .;8~4~9..,5c..~..-. -,;~-
·~==- 0.256580
···-··... ····- 1.720743 ~,0?~?··1- . ·- ._..-....-.--················•----
22 0:2564320..68580SL_3J21237.L_71714••4l._~i?7?~?r.2:soa32:J~2-.:~1.~71(3.·.7··.:·.9::·:::···:2.··::.:.l:.::..·:::
~~=~-= 23 1o0.2.255662..19._.·717.o03..66885438..05J.·._601i·1:•31·1.3914.7.5!.8.0x..31-::·6-7·711.3_..8?..7~.1[.2~-.~~::?20.~6.8.3--69-60·22..:449992817·J6·1[22..~77~946..9....4·..[1•.337~6.77?.4..5.4·-.·
-I_2_5.c.........1.. ·0:2560l?6:0?8443·01l1.~~1·r6x3:4?5?..~).0i~59~54 2.48511'1[2.7874143.725·•1
I 26 1·0:25.5..91.0.5.56.84043[i~.~-14-·91ii7o2sGia···l·2·:·o··?·?·..?.~:.~2._:~.j.~i~~~=[:2:J~:?~~~-~---1__3_._70_66
r1··22i s_-_-._.l?._?..::2~s55~s·.?s·.J~s1oo~:.:G68a3.33658:·3r1~1x:.~i:7i:~?2::~5~.2...J7~.x~.-..::.i??.?~1.:...=J.1.[·i.~.2o·~.4~.o1as.~41ia·-3··2~·::-4:-?6.?.~7..?-.1.:.:4.1_[122.-:?~~ii~o2G~.a33·..-6~..-:8~·=9~·.·_6.~·.:~...-....
1 29-- ··········· .~. ;~s-~~~o~.6--8.~30=.4.'.:4.1.1:iii4.341·.-6.9912I7!:o:5.~~.,~2·.-4-6=2~0·2[~~:~~~··:~:~~·5:·94:.....
I . 30 ....0..25560,5·a·:6827J5i6:iio4is...-.~. ~9.i2._~_..-~2.042.2..7...12...4..5..7..26I.2..7. 5000...3...6..4. 6._.0_ _
1 inf 0.2533.4..170.674.4.·9·0:11.231..5.-.5.i.2:6448.5.14'1·.·9·5·996.·2:326i-s112··:··s·is.s.i..3...2.9..0.•.5...
1
1
|
|
10 Page 10 |
▲back to top |
APPENDIX E: The Chi-Square Distribution
b
...._.._.._.....,.·------..!
df\\p .995 l..:?.9. .?....·.?.7.-..~L. .:?5°..jL.:..?..~~.-..7150 l._. .5..0.0J'.250 ·:...,.:.:.:.:..:,.:.:.:::..··_.·~:.:..·.·:.:··.:::c;:.:0·:2:5I .010
..1..._.. L?:O??~~ 0.??:~9I?3:?::~1~7.[9o.1015~3:4~4I?L43~2330
~:0238'·9~:~34I_79.80794I~
-z-·lo.010'0io3.020100.-0506l[4o~ici2lrso9:-2ioTno.57536-fi.38[622.797259
7.377796.-2l io~ .i059663
3 0.0717i2?•1~483.1~~i1o5:s3.5o1i8l5o:5843/17.21215[23.365J947.rn831416.2s1J3.79.81417:93.348410_11.3·4141827.83816
. .:.~~:2:._?~9[9o::~~~:?4~i~~l2-?-":.]?.2._~._1?I1?.06361I2T9-!2.153-6.3=5616.95.3.8..5!72:779..4.~.4~4~?..?.·I.131..43219~:.~?.l~.~?~.?~I8.~??~.I
Jii:G2..s. .Gs [iG.74960 ·~--· o.4~1~ 10.55430 10.83121 [1.145481[1.61031 J2.67460 ~.35146
):23636 _I11.07050, 12.83250 ... 15.08627
1
1
1
j 6 :o.67573 o.87209 11.2.3734 1.63538 1 12.20413 [3.45460 I 5.34812 lt84o8o I 10.644641 12.59159 [ 14.44938; 16.81189 1118.54758
1
··-7.:~~:1·0:1~:3948494[l12~i.-6:2?-3'19.6.0.~4?~~?...?-§.7sf-~_·.11r;322:,:74~3..8~29.6~i454~.4~2-:15,:.4.~·8:[5?J1..'?34~411~192.0·-3:--71J11[5i1i.302G17is'0[rii1'41As·::0s6oJr7E~n3-:~°1-3:,~.J:-~.2~?50f.:]~:~0?9.0~i~2.~2o41..11J2.7:;7;1~74~9-~]
-·9-~ii-:•73419.32·:asii'li2o.ioo3_93.3251f1d1.1G.s..i16s:a;;·s1'sa:3i 42aIi11.3881i71;5;:6a3·61166.9181 ;9:8;;:02·21i2·i~Ei.s1s2.939.58·9135
J __!0 12.15586 l55821
3.24697
1
'J3,94030 __.14.86518 "16.73720 ~.34182
][12.54886
15.98718 j 18.307o4 J 20.48318J23.209251l25.18818
·
.~~2L.6.0321/2~-:?~.3...3~.88157·154.574J1851:~?.?J.7?.85.841l4:~.3.~1??.J1~l:.?3.·.·27...7?~.:5?.6.?6.7~.~.~]2:~..J:9-~~.?i..?:?~2J.~2~6?.7.J5685
--12r-~-:-o?.~~a.~5-7105174..4?3.J7's9:.~~.~lo6_.:i3]~3f~ao:43~i.2~·.l1I1.14..~34~0=~3?~2..'.54912315:·0·2263·.~3;3;~6Ii·66.:6·21i12i?8·:1299~2
-n 3.5650[34.1069s2~ooa7li5s:.sii1s[67.04150-~~2f91920.373976lls.91893.981]i9i'fi'22J:2i642.7033·s2s7a.,688251Ji9:a1947
144~0746174~.660453.6287~35706]317,78-·915!310.16[153.i3-3927117[.21i1:06G9342134.6. 842769.711829i517412341] .31935
2 ~6.?~..?1.,.~...:..~.2...6.~...2.36.2~114.?.~.~?1~.8~.-5.:46·[1716.036I_514~:3...J3.~. ._~~28.:6..J.1~2.°2...3~01721.:3..:9.9~-.5?7::..i~J1~33.0.9,:-5.7;[.37.2~.1:~?1.3.2_
16 s.142]2~1.8~:z'~-6.9076[76.961G9s:}-j~2.J.~114.912[2125.3385(1931i6.28.836:?~_l12863.~9!258.j.38453.5j:]9~9J,933~J6719
17 5.697262.4077167.564189.67176-1[10l'i.0:18.5719/9169.3338I1280:488681[24.76904I 3T02.179:s1a30n311.]408[6365..71847
18 6.2648[07.0-148~.123071f95:390411160··.864r9143.67512197.33117:9201.6]0.42859.98942112183.18.65923J630348.805]371.156.45
-19-6M3.9i7l?.:6.3_.21. ?~,·39°._6[?12.a.'.1].[1ii.:?G.0s1o.!9~i-:.l·5~.[2i.s?-o.337,262s:·i[1is1i2-!7.2?_3l,j~o?:i~31:.s33-~~5~3.31.3I13.68.1598028275.
·2.[~4:33-81[48,260~19~:5~9-0- 7!'8~o.85?1[B1_i 2,:4_l2~.:6~1~:.5'.1~7372] ~J,233. .8271~298-:J~~j311.9.4~1.03~.~31.]6.•9_.63-17' :56612339~~9~685
··21'·8-.-0336[5a.8972100_.2821[9it0.591..I3[13.23..91660.344[3280..337 7[243.934,2798.]61·5[1039.2.5.7·305.7417·81838 .93·124117.40106
. 22 .8.6427I~2~. :?.:~_:.9-11l~0.29.8~2~I3j312.4.~.0.?4~1l.419.?:2..•132.91-..3~32j.7.20.64.:.?l.~3~2-~71. .333.2.9.~2.4I34647.807I:1.?.:2._~l_~:.32.._:?6.~.l5..6.5
23 9_._26r01402:1·9~72·ri~~~s.ss11~~:0l9l8o.s113,71~3~:08~4376~8(851[2.7.1~134·132:0o3689,aD.?].l5436153.:61~7824~6·144.i8128
24 9.88623-"["101.2ss.4G031·[61i'5:i.848i1453..6[581698:.o37.[2253.33/2687:3241Il1353.1%·f2346.41.53093.364[4028:979I18425.558, 51
r~.~~3-~~:: 2s 110.51l9j1615.5231938.119[1742.611ll4l61.473[4119.93[912344.336[259.33.181_3845.3[8,3175.96521480:64164447.3141[1406.927I 89
:2: ~.1-...1:.:.1.[162?:.1~94...8~1~5 ~:jji~s.3~7~911[?'6i.i:··,2si'ss1 l:.~.-3_.3~.§6~..~~3~435.~:]?~3i~..~1-.·.?~J~~1~.J :~s:~4j1.~~
..2. 7I-~l-~~75_9-.f~14:-.85?_8.?.r5..~01~._~6.1[153-1:14103.1J9~01~.7-:l.2?64.03..3.IS._L~532~84~1~·:,?.~~14202.1- 13:2.?3~~5j146.~~2[?44?··.61.4I492
·-2.s.1i2·:4611:1334.-5-6··41751.307li8l66.927181a8: ~913!292.4-:6512771.6336IJ2332.G2·3074.991isI9421:i3il14.44.460,4-789:278112s4o-.·993138
29 ..
30
11133..172816j1174524..925536I11446G65.:074·79I10o77.f7]0J~8I1I[18329.7074.·69.7·2.s76.19l146292..3:2..:35:?61.l16?:~2.5~~~9~.~:~~~~~~1~7.?31.~.0~J9;3]1~~?13-9~.9::,~~..?2.i?.i]8~o:-4]?3~.77.7/~24~9577:.2-J~24~21~?4?9:.9.9~~-.?5:.8~.8..~7?I;~~858~_~2!.:3J_.1 3.5~2