 |
ASP610S-ASP611S - APPLIED STATISTICS AND PROBABILITY - 1ST OPP - JUNE 2022 |
|
|
1 Page 1 |
▲back to top |
p
NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
FACULTY OF HEALTH, APPLIED SCIENCES AND NATURAL RESOURCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: BACHELOR OF COMPUTER SCIENCE
QUALIFICATION CODE: 07BOCS
LEVEL: 6
COURSE CODE: ASP610S / 611S
COURSE NAME: APPLIED STATISTICS & PROBABILITY
SESSION: JUNE 2022
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 90
EXAMINER:
MODERATOR:
FIRST OPPORTUNITY EXAMINATION
MR AJ ROUX
MR E. MWAHI
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 done in blue or black ink.
PERMISSIBLE MATERIALS
1. Non-programmable calculator without a cover.
ATTACHMENTS
1. Statistical Tables ( Z-tables)
Page 1 of5
|
|
2 Page 2 |
▲back to top |
Question 1 [10]
1.1 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]
1.2 Asample 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 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]
1.4 Weight is a
variable
a) Continuous
b) Discrete
c) Ordinal
d) Interval
[2]
1.5 Researchers do sampling because of all of the following reasons except
a) Reduce cost
b) More time effective
c) Sampling is interesting
d) Easy to manage due to manageable logistics requirements
[2]
uestion 2
20
The data below shows test scores in ASP611S for a random sample of students
86,
72,
23,
56,
62,
94,
48
Use the data provided to fin the following:
2.1 The average score
a) 64
b) 66.5
c) 63
d) none of the provided
[2]
2.2 The modal score
a) 86
b) no mode
c) 23
d) none of the provided
[2]
2.3 The median score
a) 72
b) 62
c)no median d) none of the provided
[2]
2.4 The range of the scores
a) 72
b) 73
c) 71
d) none of the provided
[2]
Page 2 of 5
|
|
3 Page 3 |
▲back to top |
2.5 The first quartile of the scores
a) 62
b) 48
c) 71
2.6 The third quartile of the scores
a) 88
b) 94
c) 62
2.7 The inter-quartile range for the scores
a)O
b)38
c)17
2.8 The Quartile Deviation for the scores
a) 4
b) 8
c) 12
2.9 The variance for the scores
a) 574.3
b) 525.5
c) 440.0
2.10 The coefficient of variation for the scores
a) 25.5%
b) 75.5 %
c) 38%
d) none of the provided
d) none of the provided
[2]
d) none of the provided
[2]
d) none of the provided
[2]
d) none of the provided
[2]
d) none of the provided
[2]
QUESTION 3 [15 Marks]
Consider the contingency table below.
Undergraduate
Graduate
Postgraduate
Production |
92
19
15
Sales | Management | Others
76
24
65
15
62
41
26
37
28
If one employee is randomly selected, what is the probability that he or she:
3.1) is either a postgraduate or belongs to sales department?
[3]
3.2) is an undergraduate given that he belongs to production department?
[4]
3.3) is neither a postgraduate nor belongs to management department?
[4]
3.4) — does not belong to sales department given that he is not a graduate?
[4]
Page 3 of 5
|
|
4 Page 4 |
▲back to top |
QUESTION 4 [10 Marks]
Research has shown that, for a certain company, 7% of plant A products are defective, 92%
of plant B products are non-defective, 10% of plant C products are defective, and 95% of
plant D products are non-defective. Of all the products manufactured by this company, 25%
come from plant A, 15% from plant B, and 12% from plant C and the rest from plant D. An
inspector has just randomly selected one product from the warehouse of this company.
What is the probability that it is non-defective?
QUESTION 5 [15]
The Ministry of Basic Education Namibia revealed that in a random sample of two hundred
teachers, exactly one hundred and thirty eight of them have a post graduate qualification in
education .
5.1) What part of this sample has have a post graduate qualification in education .
a) 0.96
b) 0.69
c) 1.38
d) none of the provided
(2)
When constructing a confidence interval estimate for the single unknown population
proportion {mt} of the teachers who have a post graduate qualification in education .
5.2) What critical value will be used?
a) t
b) z
c) v
d) none of the provided
(2)
5.3) Compute the Standard Error of estimate
a) 0.2139 bb) 1.0695
c) 0.0327 ~=d) none ofthe provided
(3)
If you construct a 90 % degree of confidence interval estimate for the population proportion
of teachers who have a post graduate qualification in education .
5.4) What critical value will be used?
a) 1.645
b) 1.96
é) 2.575
d) none of the provided
(2)
5.5) What will be the lower limit (LL) for this confidence interval estimate?
a) 0.05379 b)0.63620
c)0.69
d) none of the provided
(3)
Page 4 of 5
|
|
5 Page 5 |
▲back to top |
5.6) What will be the upper limit (UL) for this confidence interval estimate?
a) 0.69
b) 0.05379 = c)0.7438 ~=d) none of the provided
(3)
QUESTION 6 [20 Marks]
The marks of 600 students in Statistics test are normally distributed with mean 60 and
standard deviation of 5.
6.1) If one student is randomly selected, what is the probability that scored 53.3 and
6.2)
above?
(4)
If one student is randomly selected, what is the probability that scored 69.7 and
below?
[4]
6.3) If one student is randomly selected, what is the probability that scored between 56.1
and 73.3?
[6]
6.4) If pass mark is 50, how many students passed the test?
[6]
END OF QUESTION PAPER
Page 5 of5
|
|
6 Page 6 |
▲back to top |
APPENDIX C: The Standard Normal Distribution
z | 0.00 | O01 | 0.02 | 0.03 | 004 , 0.05| 0.06| 0.07 | 0.08 . 0.09|
0.0 {0.0000 10.0040 0.0080 0.0120 .0.0160 10.0199 10.0239 0.0279+ 0.0319 0.0359
0.1 10.0398 10.0438 |0i .0478 ;0.0517 10.0557 Z10.0596 ne 0.0636 ---— 10.0675 ;0.0714 0.0753 meer seen a enranteain Feice nT,
0.2 (0.0793 10.0832 {0.0871 {0.0910 10.0948 {0.0987 10.1026 0.1064 0.1103 0.1141
'1 0.3 (01179 10.1217 {0.1255 (0.1293 0.1331 10.1368 10.1406 10.1443 {0.1480 0.1517
j
1
0.4
[0.1554
10.1591
a(0s.1628
10.1664 10.1700 :0.1736 10.1772 10.1808 0.1844 0.1879 -
ies Ga SENS NETS ce, semper stat
STS a a SELES oe pepe
as Keno
0.5 (0.1915 10.1950 [0.1985 a 10.2019 10on.2054 stant [0.2088 10.2123 10.2157 10.2190 0.2224
0.6
0.7
{0.2257 (0.2291
{0.2580 {0.2611
(0.2324 10.2357 {0.2389 10.2422
(0.2642cremains [0.2673 10.2704 a 0274
10.2454
10.2764
101t 0..22478694
0.2517
:0.e28e2e3
‘0.2549 |
‘0.2852 ee pee eee
0.8 10.2881 {0.2910 0.2939 (0.2967 0.2995 '0.3023 0.3051 10.3078 10.3106 10.3133
0.9 [0.3159 10.3186 10.3212 10.3238 .0.3264 _ 10.3289 0.3315 (0.3340 0.3365 0.3389
1.0 103413 0.3438 0.3461 10.3485 10.3508 -0.3531 10.3554 :0.3577 10.3599 -—-.0.3621
' LL -0.3643 [0.3665 10.3686 10.3708 '0.3729 0.3749 10.3770 0.3790 0.3810 .0.3830__
12 [03849 (0.3869 [0.3888 10.3907 10.3925 (0.3944 (0.3962 10.3980 03997 (0.4015
13 0.4032 [0.4049 0.4066 0.4082 10.4099 0.4115 0.4131 10.4147 10.4162 ‘10.4177
| 14 10.4192 [0.4207 10.4222 10.4236 = ,0.4251 10.4265 0.4279 (0.4292 10.4306 10.4319,
|i 15 1i 0.4332 10.4345 ——S 10.4357 1f 0.4370 ink 10.4382 «: 0.4394 «jn10s.4a4n0e6 © «10.44~1~8 + 10.4429 «(_(0.4441 |
1.6 10.4452 10.4463 (0.4474 10.4484 10,4495 _ [0.4505 [0.4515 {0.4525 '0.4535 10.4545
| 17 0.4554 (0.4564 10.4573 10.4582 10.4591 10.4599 0.4608 ~—.0.4616 0.4625 -—«0.4633
I 18 [0.4641 10.4649 0.4656 10.4664 «0.4671 ‘10.4678 +—--0.4686 0.4693 “[oa6s9 04706
| 19 [0.4713 '0.4719 [0.4726 (0.4732 10.4738 0.4744 «10.4750 10.4756 «10.4761 —0.4767 “|
| 2.0 :0.4772 10.4778 0.4783 10.4788 = 40.4793 ,0.4798 (0.4803 0.4808 10.4812 0.4817 |
| 21 a:10.4821 1—0.4826 :10.4830 :0.4834-««'0.4838 - «0.4842 «0; .4846 «10:.4850 10.4854 10.4857. |
es a eee cee pemrenrne nmm e ee ae pect ee me neermemerriesee ened ane
bia Sa Toe
nmmnnse APSA ASU SERSeen pemme mtcomm
EES S ES eeemere
; 2.2 :0.4861
\\0.4864 10 4868 = 0.4871 “10. 4875
:0.4878
‘0 4881
:0.4884
i0 4887
0.4 4890
| 23 0.4893 10.4896 [0.4898 10.4901 0.4904 [0.4906 0.4909 “40.4911 [0.4913 0.4916;
| 24 [0.4918 10.4920 :0.4922 10.4925 10.4927 0.4929 10.4931 0.4932 10.4934 0.4936
2.5 {0.4938 10.4940 [0.4941 10.4943 10.4945 [0.4946 10.4948 0.4949 «40.4951 0.4952
2.6 10.4953 10.4955 ;0.4956 10.4957 {0.4959 [0.4960 [0.4961 0.4962 0.4963 (10.4964
2.7 10.4965 0.4966 [0.4967 | 0.4968 0.4969 10.4970 10.4971 (0.4972 10.4973 0.4974
' 28 0.4974 10.4975 10.4976 10.4977 0.4977 00.4978 (0.4979 10.4979 10.4980 “(0.4981
| 2.9
10.4981 10.4982 10.4982 [0.4983 0.4984 oon emma ees eee cee
[or ct
errr
ee eee
0.4984 10.4985 0.4985 10.4986 10.4986 ins Laatae, emeene mentee
seater eee
soe ee crweneee cere teeen,
one
ceeeen:
3.0
:0.4987
10.4987 10.4987 ‘0. 4988 ~ 10.4988 0. 4989. . ‘0.449989 “o. 4989 0. dled :0. 4990
|
|
7 Page 7 |
▲back to top |
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
-3.8 | .00007
00007
.00007
.00006
.00006
.00006
.00006
.00005
.00005
.00005
-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
.0003 1
.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
0132]
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
15151
14917
14686
14457
14231
14007
13786
-0.9 | .18406
18141
.17879
17619
.17361
.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
47210
46812
46414
www.rit.edu/asc
|
|
8 Page 8 |
▲back to top |
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
0.0 | .50000
0.1 | .53983
50399
54380
50798
54776
51197
55172
51595
55567
51994
55962
52392
56356
52790
56749
53188
57142
53586
57535
=~ 0.2 | .57926
58317
58706
59095
59483
59871
.60257
.60642
.61026
61409
0.3 | .61791
.62172
62552
.62930
.63307 ~—- 63683
64058
64431
.64803
65173
0.4 | .65542
.65910
.66276
66640
_.67003
.67364
67724
68082
68439
.68793
0.5 | .69146
.69497
69847
.70194 ~— .70540
70884
71226
.71566
.71904
.72240
0.6 | .72575
12907
h3237
73565
.73891
74215
74537
74857
75175
75490
0.7 | .75804
76115
.76424
.76730
—.77035
.77337
-77637
.77935
.78230
.78524
0.8 | .78814
.79103
79389
.79673
.79955
80234
80511
80785
81057
81327
0.9 | .81594
81859
82121
82381
82639
82894
83147
83398
83646
8389|
1.0 | .84134
84375
84614
84849
85083
85314
85543
85769
85993
86214
1.1 | .86433
.86650
86864
.87076
—.87286
87493
87698
87900
88100
88298
1.2 | .88493
88686
88877
89065
89251
89435
89617
89796
89973
90147
1.3 | .90320
.90490
90658
90824
90988
91149
91309
91466
91621
91774
1.4 | .91924
92073
92220
92364
92507
__—.92647
92785
92922
93056
93189
1.5 | .93319
93448
93574
93699
93822
93943
94062
94179
94295
94408
1.6 | .94520
.94630
.94738
94845
94950
95053
95154
95254
95352
95449
1.7 | .95543
95637
95728
95818
95907
95994
.96080
.96164
96246
96327
1.8 | .96407
96485
96562
.96638
.96712
96784
96856
.96926
96995
97062
1.9 | .97128
97193
97257
97320
97381
97441
97500
97558
97615
97670
2.0 | .97725
97778
9783 | 97882 = 97932
97982
.98030
98077
98124
98169
2.1 | .98214
98257
98300
98341
98382
98422
98461
98500
98537
98574
2.2 | .98610
98645
.98679
98713
98745
98778
98809
98840
.98870
98899
2.3 | .98928
2.4 | .99180
98956
99202
98983
99224
.99010
99245
99036
99266
99061
99286
99086
99305
99111
99324
99134
99343
99158
99361
2.5 | .99379
99396
99413
99430
99446
99461
99477
99492
99506
99520
2.6 | .99534
99547
99560
99573
99585
99598
.99609
99621
99632
99643
2.7 | .99653
99664
99674
99683
99693
99702
99711
99720
99728
99736
2.8 | .99744
99752
99760
99767 = 99774
9978]
99788
99795
99801
99807
2.9 | .99813
99819
99825
99831
99836
99841
.99846
99851
99856
99861
3.0 | .99865
99869
99874
99878
99882
99886
99889
99893
99896
99900
3.1 | .99903
99906
99910
99913
99916
99918
99921
99924
99926
99929
3.2 | .99931
99934
99936
99938
99940
99942
99944
99946
99948
99950
3.3 | .99952
99953
99955
99957
99958
.99960
99961
99962
99964
99965
3.4 | .99966
99968
99969
99970
9997]
99972
99973
99974
99975
99976
3.5 | .99977
99978
99978
99979
99980
9998]
9998 | 99982 = .99983
99983
3.6 | .99984
3.7 | .99989
99985
99990
99985
99990
99986
99990
99986
9999]
99987
9999]
99987
99992
99988
99992
99988
99992
99989
99992
3.8 | .99993
99993
99993
99994
99994
99994
99994
99995
99995
99995
3.9 | .99995
99995
99996
99996
99996
99996
99996
99996
99997
99997