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IAS501S - INTRODUCTION TO APPLIED STATISTICS - 1ST OPP - JUNE 2022 |
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p
NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
FACULTY OF HEALTH, APPLIED SCIENCES AND NATURAL RESOURCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelor of science ; Bachelor of science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BAMS
LEVEL: 5
COURSE CODE: IASS015S
COURSE NAME: INTRODUCTION TO APPLIED
STATISTICS
SESSION: JUNE 2022
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 75
EXAMINER
FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
MR. A.J. ROUX
MODERATOR:
DR. D. NTIRAMPEBA
THIS QUESTION PAPER CONSISTS OF 5 PAGES
(Excluding Statistical Tables) ..
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 dohe in blue or black ink.
PERMISSIBLE MATERIALS
1. Non-programmable calculator without a cover.
ATTACHMENTS
1. Statistical Tables ( Z-Tables & Chi-Squared Table)
2. Graph Paper
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UESTION 1
30]
‘
1.1
1.1.1)
1.1.2)
1.1.3)
1.1.4)
1.1.5)
Indicate whether each of the following variables
identify the appropriate scale of measurement:
age ofa child during an immunization
gender of an applicant attending an interview
the rank in which athletes obtained prices
the make of the cellphone which the child lost
percentage of students who passed the test
is quantitative
or qualitative,
and
(2)
(2)
(2)
(2)
(2)
1.2) For each of the following random variables, indicate whether the data type is
discrete or continuous
1.2.1) The weight of a bag of potatoes
(2)
1.2.2) The number of cars damaged in the accident
(2)
1.2.3) The distance a cyclist completed
(2)
1.2.4) The number of children with disabilities
(2)
1.2.5) The height of a ten-year old girl
(2)
1.3) [For each of these questions ( 1.3.1 — 1.3.5), Only provide the letter indicating your
correct answer]
1.3.1 Which of the following measures of central tendency can reliably be used when
dataset has outliers?
a) Mean
b) Median
c) Mode
d) All the above
(2)
1.3.2) A sample is
a) An experiment in the population
b) A subset of the population
c) A variable in the population
d) An outcome of the population
(2)
1.3.3) A parameter refers to
a) Calculation made from the population —_b) A measurement that is made from the
population __c) A value observed in the experiment
d) All of the above
(2)
1.3.4) Weight isa
variable
a) Continuous
b) Discrete
c) Ordinal
d) Interval
(2)
1.3.5) Researchers do sampling because of all of the following reasons except
a) Reduce cost
b) Can be done ina shorter time frame —_c) Sampling is interesting
d) Easy to manage due to manageable logistics requirements
(2)
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UESTION 2 [30
2.1) The Ministry of Education summarized the mathematics grades of ten thousand Grade
12 learners. The result was to categorize into the following categories A, B, C, Dand E
respectively. The following table shows data on mathematics results for a sample of 50
Grade 12 learners.
®
A
c
E
B
D
C
D
BD
C
DB DECADCDE
DCABDcBECD
B
Cc
D
C
D
C
E
A
D
Cc
Cc
B
D
D
B
D
Cc
E
B
A
2.1.1) Construct the frequency distribution for the set of qualitative datain the table. (8)
2.1.2) Construct the relative frequency distribution for the data set.
(2)
2.1.3) Draw the bar chart for the absolute frequency distribution for the data set.
(5)
2.2) |The Namibian Cycling Federation (NCF) analyzed the exercise time (in hours) spent
by asample of 530 cyclists in preparation for the popular Desert Dash.
Exercise Time
(hours)
3-<7
7-<11
11-<15
15-<19
19-<23
Number of cyclists
104
138
121
95
72
Use the data provided to calculate the:
2.2.1) mean,
(5)
2.2.2) median,
°
(5)
2.2.3) andmodalexercisetime .
(5)
QUESTION 3 [14]
The data below shows the price (in millions) for a standard size plot in an upmarket residential
suburb of Windhoek.
2012 2012 2013 2014 2015 2016 2017 2018 2019 2020
3.0
4.2
4.8
3.7
3.4
4.3
5.6
4.4
3.8
4.1
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3.1) Determine the least squares trend line equation, using the sequential coding method
with the first period coded as 1.
(8)
3.2) Use the trend line equation obtained in Question 3.1 to estimate the price for the same
plotin 2010 and 2023.
(6)
UESTION 4 [10
The quality control manager in a tyre manufacturing plant in Oshakati wants to test a
belief that the nature of defects found in manufactured tyres depends upon the shift
during which the defective tyre is produced. He therefore compiled the following two-
way pivot table showing the number of defective tyres identified by shift and by
nature of defect. Is there evidence to substantiate a claim that there is a statistical
association between the nature of defective tyres and the shift on which they are
produced?
Shift
technical
Nature of tyre defect
mechanical
material
Morning
Afternoon
Night
15
42
11
26
40
20
29
25
14
Is there evidence to substantiate a claim that there is a statistical association
between the nature of defective tyres and the shift on which they are produced? Use
a =0.05
QUESTION 5 [16]
5.1) The average cost of providing a particular service per person per day is a random
variable having a normal distribution with average of NS100 and a standard deviation
of NS22.
°
5.1.1) Calculate the probability that the cost of providing the service will be at least
NS120 per day per person.
(5)
5.1.2) Calculate the probability that the cost of providing the service will be at least
NS60 per day per person.
(3)
5.2) The Office of the Registrar has revealed that only 12 oft of every 20 students
graduate. Based upon this assumption, determine the probability that out of a
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random sample of 5 students
5.2.1) None will graduate
(3)
5.2.2) All will graduate.
(2)
5.2.3) At most one student will graduate
(3)
XXXXXXXXXXXXXXXXXX X XX XXAX XXAXX KXKX XXKXX KXXX KXXXX XAXX XXXAXKX XXX AX X KKKX XXX X XXXXKXXXX X AA XXXAXX AX XX X KKK
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The Chi-Square Distribution
ldfip | 995 990 | 975 | 950 | 900 | .750 | 500 ; 250 | 100 | 050 | 025 | .010 | 005
| 1 0.00004 /0.00016 [0.00098 {{0.00393 [0.01579 ||0.10153 {[0.45494 |1.32330 {2.70554 |3.84146 |5.02389 [6.63490 | 7.87944
| 2 [0.01003 {0.02010 |0.05064 [0.10259 [0.21072 [0.57536 {1.38629 |2.77259 |4.60517 |5.99146 | 7.37776 {9.21034 | 10.5963
| 3 [0.07172 [0.11483 [0.21580 [0.35185 [0.58437 [1.21253 |2.36597 /4.10834 [6.25139 |7.81473 | 9.34840 |11.34487 | 12.83816
| 4 Q 20699 0.29711 |0.48442 [0.71072 | 1.06362 {1.92256 13.35669 [5.38527 17.7944 |9.48773 | 1.14329 | 13.27670 | 14.86026
| 5 0.41174 0.55430 |0.83121 |1.14548 [1.61031 |2.67460 | 4.35146 | 6.62568 | 9.23636 |11.07050 | 12.83250 |15.08627 | 16.74960
| 6 |0.67573 [0.87209 | 1.23734 |1.63538 {2.20413 [3.45460 |5.34812 | 7.84080 | 10.64464 | 12.59159 | 14.44938 | 16.81189 | 18.54758
| 7 (0.98926 {1.23904 [1.68987 {2.16735 [2.83311 | 4.25485 [6.34581 |9.03715 | 12.01704 | 14.06714 | 16.01276 | 18.47531 | 20.2774
| 8 [1.34441 | 1.64650 | 2.17973. |2.73264 3.48954 | 5.07064 |7.34412 | 10.2185 | 13.36157 | 15.50731 | 17.53455 |20.09024 | 21.95495
|9
| 10
{L| 41..1735459836
[2.08790
| 2.55821
[2.70039
]3.24697
|3.32511
|3.94030
| 4.16816
| 4.86518
[5.89883
6.73720
-
|8.34283
[9.34182
| 11.38875 | 14.68366 | 16.91898 | 19.0227 | 21.665|99 23.58935
fia.saee |[1598718 | 18.30704 | 20.48318 | 123, 20925 |25.18818
Far | 2.60322 {3.05348 [3.81575 [4.57481 |5.57778 | 7.58414 11034100 | 13.70069 | 17.27501 | 19.67514 |21.92005 |24.72497 | 26.75685
(32 |5.07382 |3.57057 |4.40379 [5.22603 [630380 (| 8.43842 1i 11.34P0e32 || 14.84540 [1854935 | | 21.026|07 23.3366| 26.2197 |28 19952
[13 I3.56502 [4.10692 [5.00875 [5.89186 i[7.04150 |9.29907 [12.2276 /15.98391 | 19.81193 |22.36203 | 24.73560 |27.6882a5 a|. 2r19n47
114 |4.07467 '4,66043 |5.62873 [6.57063 [7.78953 | 10.1653: | 13.3397 117.11693 Ea aciia (ameeirs [Sima bs, 14124 13151935
/-15 [4.60092 [5.22935 16.26214 |7.26094 |8.54676 |11.03654; 14.33886 | 18.24509 |22.30713 |24.99579 |27.48839 130.5791 (3rs 80132
16 © 5.14221 |5.81221 [6.90766 [7.96165 9.31224 |11.912'~ | 15.33850 | 19.3686 |23.54183 |26.29623 |28.84535 | 31.9993 | 34.26719
1i 17.15,69722 [6.40776 | 7.56419 ||8.67176 [ia08s19 [12.79193 116.3818| 20.48868 | 24.76904 |27.58711| 30.1910|1 33.4066 [38.71847
is 6.26480 [7.01491 [8.23075 [9.39046 10.86494 [8 67524 |17.33790 z 60489 [25 98942 [28 86930 | 31.52636 34 9531 [37.15645,
19 6.84397 [7.63273 | 8.90652 | 10.1701 {1.65091| 14.56200 | 18.33765 |22.71781 |27.20357 |30.14353 | 32.8523 ry | 38.58226
| 20 |7.43384 8.26040 | 9.59078 | 10.85081 | 12.44261 | 15.45177 , +9.33743 |23.82769 |28.41198 |31.41043 | 34.16961 |37.56«2? |39.99685
| 21 |8.03365 [8.89720 | 10.28290 |11.59131 | 13.23960 | 16.34438 | 20.33723 |24.93478 |29.61509 |32.67057 | 35.47888 |38.93217 | 41.40106
| 22 [8.64272 |9.54249 | 10.98232 |12.33801 | 14.04149 | 17.23962 | 21.33704 |26.03927 | 30.81328 |33.92444 | 36.78071 | 40.28936 | 42.79565
|\\ 23 [9.26042 |10.19572 1| 1.68855 |13.09051 | 14.84796 | 18.13730 [2 33688 |27.14134 | 32.00690 |35.17246 | 38.07563 | 41.63840 | 4.18128
| 24 |9.88623 | 10.85636 | 12.40115 [13 84843 | 15.65868 | 19.03725 |23.33673 hoe.24115 | 33.19624 | 36.41503 |39.36408 | 42.97982 | 45.55851
| 25 | 10.51965 | 11.52398 |13.11972 | | 14.61141 | 16.47341 | 19.93934 (34.33658 | |29.33885 | 34,38159 |37.65248 | 40.64647 | 44.31410 | 46.92789
i|i 26 (1.16024 | 12.19815 | 13.84390 | 15.37916 |17.29188 | 20.84343 |25.33646| |30.43457 | 35.56317 |38.88514 | 41.92317 | 45.64168 | 48.2898
|[27 |11.80759 | 12.87850 | 14.57338 | 16.15140 | 18.1390 |21.74940 |26.33634 r13152841 36 74122 | 40.1327 (43. 19451 [46, 96294 | 49.64492
28 |12.46134 |13.56471 | 15.30786 |16.92788 | 18.93924 |22.65716 |27.33623| 32.62049 |37. 91592 (41. 33714 a 46079 148. 27824 | 50. 99338
| 29 113.1215 |14.25645 | 16.04707 | 17.70837 | 19.76774 | 23.56659 | 28.33613 |33.71091 | 39.08747 (4255607 | | 45.72229 (49.58788 | 52.33562
| 30. |13.78672 |14,95346 | 16.7907 | 18.4926 | 20.59923 | 24.47761 | 29.33603 34.7974 | 40.25602 | 43.77297 | 46.97924 |50.89218 | 53.67196
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APPENDIX C: The Standard Normal Distribution |
iz | 0.00 | 0.01 | 0.02 0.03 0.04 0.05 0.06 | 0.07 | 0.08 0.09 ,
0.0 10.0000 0.0040 {0.0080 ;0.0120 0.0160 10.0199 10.0239 (0.0279 {0.0319 0.0359 -
Fp. (0.0398 10.0438 10.0478 ,0.0517 0.0557 10.0596 10.0636 10.0675 {0.0714 0.0753
(0.2 (0.0793 0.0832 {0.0871 0.0910 0.0948 + 10.0987 10.1026 0.1064 {0.1103 0.1141 _
(03 (01179 (0.1217 [0.1255 0.1293 (0.1331 0.1368 ‘0.1406 (01443 10.1480 0.1517
0.4 [0.1554 10.1591 ,0.1628 0.1664 0.1700; 01736 10.172 (0.1808 ‘0.1844 "0.1879
0.5 (0.1915 0.1950 [0.1985 0.2019 10.2054 0.2088 10.2123 0.2157 0.2190 0.2224
(0.6 (0.2257 /0.2291 {0.2324 10.2357 10.2389 0.2422 ‘0.2454 '0.2486 0.2517 (0.2549
a7 jo2ss0 ‘02611 (0.2642 02673 02704 02738 (3768 Lo2794 (0.2823 92852
08 10.2881 (10.2910 0.2939 0.2967 0.2995 '0.3023 0.3051 (0.3078 10.3106 03133 3
0.9 30.3159 (0.3186 0.3212 0.3238 + -0.3264 «10.3289 ~=—-0.3315 0.3340 -0.3365 0.3389
To losis 038380. 3461 03485 103508 03531 (0.3554 03577-03599 0.3621
“qa 03643103665 0.3686 10.3708 10.3729 0.3749 “0377003790 {0.3810 0.3830
i 1.2 10.3849 0.3869 «10.3888 + :0.3907 10.3925 0.3944 10.3962 10.3980 0.3997 .0.4015_ |
r 13 10.4032 (04049 0.4066 {0.4082 0.4099 0.4115 0.4131 10.4147 (04162 (0.4177
| 14 (0.4192 10.4207 10.4222
| 1.5 10.4332 0.4345 —:0.4357
“6s fo4as2 0.4463 .0.4474
| 17 10.4554 0.4564 10.4573
[18 (0.4641 [0.4649 0.4656
10.4236 0.4251 (0.4265 (0.4279 (0.4292 10.4306 04319
«10.4370 10.4382 «(0.4394 —0.4406 ‘oasis {0.0029 (0.aaai “|
(0.4a84 (0.4495 0.4505 (0.4515 104525 (0.4535 0.4545
10.4582 04501 0.4599 0.4608 36 16 ‘0.4625 0.4633,
10.4664 «10.4671 «10.4678 04686 0.4693 (0.4659 10.4706
| 4.9 10.4713 0.4719 (0.4726 10.4732 10.4738 ~Oajaa” (0.4750 10.4756 10.4761 0.4767 |
; 2.0 (04772 0.4778 0.4783 10.4788 0.4793 ,0.4798 0.4803 (0.4808 10.4812 04817 |
| 241 10.4821 10.4826 10.4830 © 0.4834—«'0.4838 0. ia (04846 0485004854 (0.4857 |
22 104861 10.4864 04868 0.4871 (04875 lo4g7@ {0.4881 04884 (0.4887 40.4890
. 23 10.4893 0.4896 {0.4898 “fo.a5oi 04908 0.4906 04909 0.4911 0913. “Da5i6 7
| 24 [0.4918 10.4920 0.4922 0.4925 0.4927 010.. 4929 (0.4931 (0.4932 “04938 0.4936
; 2.5 (04938 [0.4940 (0.4941 10.4943 10.4945 0.4946 (0.4948 ‘0.4949 0.4951 10.4952
' 2.6 [0.4953 10.4955 :0.4956 10.4957 10.4959 10.4960 (0. ag61 0.496) 080. 4964 |
27 {0.4965 ‘0.4966 (0.4967 -0.4968 0.4969 10.4970 0 49710. on 0a 0.A974
"7.8 :04974 0.4975 0.4976 (0.4977 04977 0.4978 .0.4979 0.4979 04980 0.4981
| 29 10.4981 10.4982 ued 0.4983 | aged “10.4984 “ipasss 0498s 94986 (0.4986
30 04987 0.4987 0. eT (0 4988 0.49880, i989 0.4989 “Toa4989 "0.4590 | 0.4990
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See eames
STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score.
Z
00
-01
02
.03
.04
05
06
07
-08
09
-3.9 | .00005
.00005
.00004 = .00004
.00004
00004
.00004
.00004
.00003
.00003
j
-3.8 | .00007
00007
00007 = .00006
.00006
.00006
.00006
.00005
.00005
.00005
a
-3.7 | .00011
00010
.00010
00010 = .00009
.00009
.00008
.00008
00008
.00008
-3.6 | .00016
.00015
00015
00014
00014
00013
.00013
00012
.00012
00011
-3.5 | .00023
.00022
00022
00021
00020
00019
00019
.00018
00017
00017
-3.4 | .00034
00032
00031
.00030 = .00029
00028
00027
.00026
.00025
.00024
-3.3 | .00048
00047
~=—.00045
.00043
00042
00040
00039
.00038
.00036
00035
-3.2 | .00069
00066
00064
.00062
.00060
00058
.00056
00054
.00052
.00050
-3.1 | .00097
.00094
.00090
.00087 .00084
00082
.00079
00076
.00074
.00071
-3.0 | .00135
00131
.00126
00122
_—«.00118
00114
00111
00107
—_—«.00104 .00100
-2.9 | .00187
.00181
00175
.00169
00164
00159
00154
00149
00144
00139
-2.8 | .00256
00248
00240
.00233
00226
00219
00212
.00205
00199
00193
-2.7 | .00347
.00336
00326
00317 = .00307
00298
.00289
.00280
00272
00264
-2.6 | .00466
00453
00440
.00427
.00415
00402
00391
00379 = .00368
00357
-2.5 | .00621
00604
00587
00570
~——.00554
00539
.00523
00508
00494
00480
-2.4 | .00820
.00798
.00776
.00755
.00734
00714
00695
.00676
00657
.00639
-2.3 | .01072
.01044
01017
=—-.00990 = .00964
.00939
00914
00889
.00866
00842
-2.2 | .01390
.01355
01321
01287 = 01255
01222
01191
.01160
01130
01101
-2.1 | .01786
.01743
.01700
01659 = .01618
01578
01539
.01500
01463
01426
-2.0 | .02275
.02222
02169
02118
02068
02018
01970
01923
.01876
01831
-1.9 | .02872
02807
02743
02680
.02619
02559
.02500
02442 = .02385
02330
-1.8 | .03593
03515
03438
03362
.03288
03216
03144
.03074 ~~ .03005
02938
-1.7 | .04457
.04363
04272
=.04182 = .04093
04006
03920
03836
03754
03673
-1.6 | .05480
05370
05262 = .05155
05050
04947
04846
.04746
04648
04551
-1.5 | .06681
06552
06426
.06301
.06178
.06057
.05938
05821
05705
05592
-1.4 | .08076
.07927
.07780
.07636
07493
07353
07215
.07078
06944
06811
-1.3 | .09680
09510
09342
09176 = .09012
08851
08691
08534
08379
08226
-1.2 | .11507
11314
11123
10935
10749
.10565
.10383
10204
.10027
09853
-1.1 | .13567
.13350
13136
12924 = 12714
12507
.12302
12100
.11900
11702
-1.0 | .15866
15625
15386
S151
14917
14686
14457
14231
14007
13786
-0.9 | .18406
18141
.17879
17619
.1736]
.17106
16853
.16602
16354
16109
-0.8 | .21186
20897
.20611
.20327
~—-.20045
.19766
19489
19215
18943
18673
-0.7 | .24196
23885
.23576
.23270 = -.22965
.22663
.22363
.22065
.21770
21476
-0.6 | .27425
.27093
.26763
26435
.26109
25785
25463
25143
24825
24510
-0.5 | .30854
30503
30153
29806
29460
29116
28774
28434
28096
_—.27760
-0.4 | 34458
34090
33724
33360 = .32997
32636
32276
31918
31561
31207
-0.3 | .38209
37828
37448
.37070
36693
36317
35942
35569 = 35197
34827
-0.2 | .42074
-41683
41294
40905
40517
40129
39743
39358 = .38974
38591
-0.1 | .46017
45620
45224
44828
44433
44038
43644
43251
42858
42465
-0.0 | .50000
49601
49202
48803
48405
48006
47608
AT210
_—.46812
46414
www.rit.edu/asc
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STANDARD NORMAL DISTRIBUTION: Table Values Represent
Z
00
01
.02
03
04
0S
0.0 | .50000
50399
50798
51197
51595
51994
0.1 | .53983
0.2 | .57926
54380
58317
54776
58706
55172
59095
55567
59483
55962
59871
0.3.] .61791
.62172
.62552
.62930
63307
63683
0.4 | .65542
.65910
.66276
66640
__.67003
.67364
0.5 | .69146
.69497
69847
70194
.70540
70884
0.6 | .72575
72907
.73237
——.73565
73891
74215
0.7 | .75804
76115
.76424
.76730 ~~ .77035
.77337
0.8 | .78814
.79103
79389
.79673
79955
80234
0.9 | .81594
81859
82121
82381
82639
82894
1.0 | .84134
84375
84614
84849
85083
85314
1.1 | .86433
.86650
86864
.87076
87286
87493
1.2 | .88493
88686
88877
89065
8925]
89435
1.3 | .90320
.90490
.90658
.90824
90988
91149
1.4 | .91924
92073
92220
92364
92507
92647
1.5 | .93319
93448
93574
93699 = 93822
93943
1.6 | .94520
.94630
94738
94845
94950
95053
1.7 | .95543
95637
95728
95818
95907
95994
1.8 | .96407
96485
96562
.96638
96712
96784
1.9 | .97128
97193
97257
.97320
97381
97441
2.0 | .97725
97778
9783 |
97882
97932
97982
2.1 | .98214
98257
98300
98341
98382
98422
2.2 | .98610
98645
98679
98713
98745
.98778
2.3 | .98928
98956
98983
99010
99036
99061
2.4 | .99180
99202
99224
99245
99266
99286
2.5 | .99379
99396
99413
99430
.99446
9946]
2.6 | .99534
99547
99560
99573
99585
99598
2.7 | 99653
2.8 | .99744
99664
99752
99674
99760
99683
.99767
99693
99774
99702
9978]
2.9 | .99813
99819
99825
9983]
99836
99841
3.0 | .99865
99869
99874
99878
99882
99886
3.1 | .99903
.99906
99910
99913
99916
99918
3.2 | .99931
99934
99936
99938
99940
99942
3.3 | .99952
99953
99955
99957
99958
99960
3.4 | .99966
99968
99969
99970
9997]
99972
3.5 | .99977
99978
99978
.99979
99980
9998]
3.6 | .99984
99985
99985
99986
99986
99987
3.7 | .99989
99990
99990
99990
9999}
99991
3.8 | .99993
99993
99993
99994
99994
99994
3.9 | .99995
99995
99996
99996
99996
99996
AREA to the LEFT
06
07
52392
52790
56356
60257
56749
60642
64058
6443]
67724
68082
.71226
.71566
74537
74857
.71637
.77935
80511
80785
83147
83398
85543
85769
87698
.87900
89617
89796
91309
91466
92785
92922
94062
94179
95154
95254
.96080
96164
96856
96926
.97500
97558
98030
.98077
98461
98500
98809
98840
99086
99111
99305
99324
99477
99492
99609
99621
99711
.99788
99720
99795
99846
9985]
99889
99893
99921
99924
99944
99946
9996)
99962
99973
99974
9998 | 99982
99987
99988
99992
99992
99994
99995
99996
99996
of the Z score.
-08
09
53188
53586
57142
.61026
1535
61409
.64803
65173
68439
68793
.71904
72240
.79175
.75490
78230
78524
81057
81327
83646
8389|
85993
86214
.88100
88298
89973
90147
91621
91774
93056
93189
94295
94408
95352
95449
.96246
96327
96995,
97062
97615
97670
98124
98169
98537
98574
.98870
98899
99134
99158
99343
99361
99506
99520
99632
99643
99728
99801
99736
99807
99856
9986|
99896
99900
99926
99929
99948
99950
99964
99965
99975
99976
99983
99983
99988
99989
99992
99992
99995
99995
99997
99997