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BBS611C- BASIC BUSINESS STATISTICS- 1ST OPP- NOV 2023 |
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nAmlBIA
UnlVERSITY
OF SCIEnCE Ano
TECHnOLOGY
HAROLDPUPKEWITZ
GraduateSchoolof Business
FACULTY OF COMMERCE; HUMAN SCIENCES AND EDUCATION
HAROLD PUPKEWITZ GRADUATE SCHOOL OF BUSINESS
QUALIFICATION: DIPLOMA IN BUSINESS PROCESS MANAGEMENT
QUALIFICATION CODE: 06DBPM LEVEL: 6
COURSE CODE: BBS611 C
COURSE NAME: BASIC BUSINESS
STATISTICS
SESSION: NOVEMBER 2023
DURATION: 3 HOURS
PAPER: PAPER 1
MARKS: 90
FIRST OPPORTUNITY EXAMINATION -QUESTION PAPER
EXAMINER(S) Mr. A. Roux
MOD ERA TOR: Mr. J. Amunyela
INSTRUCTIONS
1. Answer ALL the questions.
2. Write clearly and neatly.
3. Number the answers clearly.
PERMISSIBLE MATERIALS
1. Examination paper
2. Examination script
3. Scientific calculator
ATTACHMENTS
1. Standard Normal Probability Distribution Table
2. 1 x A4 Graph Sheet
THIS QUESTION PAPER CONSISTS OF 6,PAGES (INCLUDING THIS FRONT
PAGE)
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QUESTION 1
[ 10 X 2 = 20]
1.
A numerical value used as a summary measure for a sample, such as sample mean,
is known as a
A. population parameter
B. sample parameter
C. sample statistic
D. population mean
E. None of the above answers is correct.
2.
If a data set has an even number of observations, the median
A. can not be determined
B. is the average value of the two middle items
C. must be equal to the mean
D. is the average value of the two middle items when all items are arranged in
ascending order
E. None of the above answers is correct
3. The standard deviation of a sample of 100 observations equals 64. The variance of
the sample equals
A. 8
B. 10
C. 6400
D.4096
E. None of the above answers is correct.
4. The variance of a sample of 81 observations equals 64. The standard deviation of the
sample equals
A.O
B.4096
C. 8
D. 6,561
E. None of the above answers is correct.
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Case 1 : Consider the result of a fictional Stats final exam taken by 155 students, as
given in the following relative frequency distribution:
Grade
Less
50-59
than 50
60- 69 70- 79 80- 89 90-
100
frequency 35
40
30
25
15
10
5. Refer to Case 1- How many students received at least a 70 in this exam?
A.25
8.50
C. 25
D.30
E.40
6.
Refer to Case 1- How many students received at most a 59 on this exam?
A.10
B.45
C. 75
D.40
E.66
Case 2: The following data show the number of hours worked by 200 statistics students.
Number of Hours Frequency
HOURS
0 --- 9
10 ---- 19
20 ---- 29
30 ---- 39
# Students
40
50
70
40
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7.
Refer to Case 2. The class width for this distribution
A. 9
B.10
C. 11
D. varies from class to class
E. None of the above answers is correct.
8.
Refer to Case 2. The number of students working 19 hours or less
A. 40
B.50
C. 90
D. can not be determined without the original data
E. None of the above answers is correct.
9.
Refer to Case 2. The relative frequency of students working 9 hours or less
A. 0.2
B. 0.45
C. 40
D. can not be determined from the information given
E. None of the above answers is correct.
10. Refer to Case 2. The cumulative relative frequency for the class of 10 - 19
A.90
B. 0.25
C. 0.45
D. can not be determined from the information given
E. None of the above answers is correct.
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QUESTION 2
[16]
The distance traveled (in kilometers) by a courier service motorcycle on 30 trips were
recorded by the driver.
224 219 221 227 220 217 217 232 222 226
218 213 223 230 210 213 218 222 234 216
218
223 215 219 228 225 225 220 217
215
2.1) Use the data provided above to construct a frequency distribution table with 210 as
the lower limit of your first class interval and a constant width of four (4) units for all
intervals.
(8)
2.2) Construct a histogram and a polygon of the frequency distribution,
(8)
QUESTION 3
[24]
The Namibian Agricultural Union compiled a record of rainfall recorded over 56 farms over
the past three months. The information is displayed in the table below:
Rainfall (mm)
3-<7
7-<11
11-<15
15-<19
19-<23
Number of farms
12
24
14
9
1
3.1 Find the mean rainfall
[5]
3.2 Find the median rainfall
[6]
3.2 Find the modal rainfall
[6]
3.4 Standard deviation in the rainfall
(7)
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QUESTION 4
[301
4.1) Pulse rates of adult men are approximately normally distributed with a mean of 70
and a standard deviation of 8. What is the probability of selecting only one man with
pulse rate of .....
4.1.1) 74.9 and higher
(4)
4.1.2) 64.1 and lower
(4)
4.1.3) 82.3 and lower
(4)
4.1.4) What is the probability that the average pulse rate for a sample of four men will be
between 66.8 and 72.7 (inclusive)
(8)
4.2) Three airlines serve a small town. Airline A has 50% of all the scheduled flights,
where-as airline B has 30% and airline Chas the remaining 20% of all scheduled
flights. Their on-time rates are 80%, 65% and 40% respectively. An airplane has just
left on time.
Let A={airline A}, B={airline B}, C={airline C}.
s
B
D
·4.2.1) What is the probability that an airplane has left on time?
(6)
4.2.2) If an airplane left on time what is the probability that it belonged to airline A (4)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
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Z-Table
The table shows cumulativeprobabilitiesfor the standardnormalcurve.
Cumulative probabilities for NEGATIVE z-values are shown first. SCROLL
DOWNto the 2nd page for POSITIVEz
z
.00
.01
.02
.03
I -3.4 .0003 .0003 .0003 .0003
' -3.3
I -3.2
! -3.1
i -3.0
.0005
.0007
.0010
.0013
.0005
.0007
.0009
.00'13
.0005
.0006
.0009
.00·13
.0004
.0006
.0009
.0012
! -2.9 - .001~
. ..--2.8- .. .0026
-2.7 .0035
.0018
.0025
.0034
.0018 .00'17
.0024. . - .0023
.0033 .0032
. .-2-·.6
! -2.5
.00.4. 7- . .0045 - .0-0-44 .. .0043 '
.0062 .0060 .0059 .0057
l -2.4 .0082 .0080 .0078 .0075
; -2.3 .0107 .0104 .0102 .0099 '
} -2.2 .0139 .0'136 .0'132 .0·129
',
'
-2.1
..-2.0-
-1.9
.0179
- .0-22. 8
.0287
.0'174
.0222
.028'1
.0170
.0217
.0274
.0'166
.02·12
.0268
---1--.8 .0359 .0351 - .0344- . .0336
i -1.7 .. - .O~.?... .04_3_6_ __.04_27-·-.-0-4·1.8-·
-1.6 .0548 .0537 .0526 .0516 '
i -1.5 .0668 .0655 .0643 .0630
I -1.4 .0808 .0793 .0778 .0764
' -1.3
l -1.2
.0968 .095'1 .0934 .0918
.1'151 .1131 .1112 .·1093
..; -1.1
' -1....0.
.1357
.1587
I -0.9... -- ----.-1· 8...41
I -0.8 .?119
I -0.7 .2420
l, ., -0.6--
I -0.5
-.274. 3 '"
.3085
•
'..
-0.4
-0.3
-0.2
.3446
.3821
.4207
.1335
·.·1-·5- 62
.'1814
.2090
.2389
.2709_
.3050
.3409
.3783
.4168
.'13'l4 .'1292
.1539 - :-1-5-1-·5
.'1788. " ·-· .1..7-62- -
.2061 .2033 I
.2358 ' .232.7.
.2676 .2643 :
.30'15 .2981 I
.3372 .3336
.3745 .3707
.4129 .4090
I -0.1 .4602 .4562 .4522 .4483
0.0 .5000 .4960 .4920 .4880
.04
.05
.0003 .0003
.0004 .0004
.0006 : .0006
.0008 .0008
.0012 I .0011
.0016 .0016
.0023 .0022
.0031 .0030
.0041 .0040
.0055 .0054
.0073
.0096
'
.0071
.0094
.0125 .0122
.0162 I .0158
.020. 7- .0202
.0262 .0256
.0329 -.0.3. 22
.04Q~ - .0401
.0505 .0495
.0618 ' .0606
.0749 .0735
.090'1 .0885
.1075 .1056
.127'I .1251
.1492 i .1469
.1736 : .171-·1-
.2005 .1977
.2296 .2266
.2-61- '1 .2578
.2946 .2912
.3300 ' .3264
.3669 .3632
.4052 .4013
.4443 .4404
.4840 .4801
.06
.07
.0003 .0003
.0004 .0004
.0006 .0005
.0008 .0008
.0011 .0011
.Q_015 .0015
.0021 .0021
.0029 .0028
.0039 .0038
.0052 .0051
.0069 .0068
.0091 .0089
.0119 .0116
.0154 .0150
.0197 .0'192
.0250 .0244
.0314 - .0307
.0392 ...0384
.0485 .0475
.0594 .0582
.0721 .0708
.0869 .0853
.1038 .1020
.1230 .1210
.1446 .1423
- .1685 . .-'1660
.1949 .1922
- .2-236 .2206
.-25..46
.2514
,-
.2877 .2843
.3228 .3192
.3594 .3557
.3974 .3936
.4364 .4325
.4761 .4721
.08
.0003
.0004
.0005
.0007
.OOID
.0014
...0020
.0027
.0037
.0049
.0066
.0087
.0113
.0'146
.0188
.0239
-
.030'1
.
.0375
.0465
.0571
.0694
.0838
.ID03
.'l190
.'14-01
.1635
.'1894
.2177
.2483
.281D
.3156
.3520
.3897
.4286
.4681
.09
.0002
.0003
.0005
.0007
.0010
.0014
.0019
.0026
.0036
.0048
.0064
.0084
.0110
.0'143
.0'183
.0233
.0294
.0367
.0455
.0559
.068'1
.0823
.0985
.1170
.'1379
, 161'1
.1867
.2148-
.2451
.2776
.3'121
.3483
.3859
.4247
.4641
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Cumulative probabilities for POSITIVE z-values are shown below.
iz
I 0.0
' 0.1
0.2
' 0.3
''
'
I
0.4
0.5
0.6
i 0.7
i 0.8
i 0.9
I 1.0
I 1.1
1.2
! 1.3
' 1.4
' 1.5
I 1.6
i'
1.7
1.8
ij 1.9
I
'
2.0
2.1
2.2
" 2.3
'
2.4
2.5
2.6
: 2.7
2.8
I 2.9
t
I
3.0
I 3.1
j 3.2
3.3
i 3.4
.00
.01
.5000 .5040
.5398 .5438
.5793 .5832
.6J79 .6217
I I .6554
.6915
.6591··--
.6950
.7257 .7291
.7580 .7611
.7881 .7910
.8159 .8"186
.84"13 .8438
.8643 .8665
.8849 .8869
.9032 .9049
_9-192 .9207
.9332__ .9345
.9452 .9463
.9554 .9564
- .9641
.9713
.9649
.9719
.9772 .9778
.9821 .9826
.9861 .9864
.9893 .9896
.9918 .9920
.9938 .9940
.9953 .9955
.9965 -- .9966. -
.9974 .9975
.9981 .9982
.9987 .9987
.9990 .9991
.9993 .9993
.9995 .9995
.9997 .9997
.02
.5080
.5478
.587"1
.6255
.6628
.6985
.7324
.7642
.7939
.8212
.8461
.8686
.8888
.9066
.9222
.9-35·--7
.9474 -
.9573
.9656
.9726
.9783
.9830
.9868
.9898
.9922
.9941
.9956
- .-9.96- 7
.9976
.9982
.9987
_999·1
.9994
.9995
.9997
.03
.S-120
_55-17
.59"10
.6293
.6664.. -
.70'19
.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
.9995
.9997
.04
.5160
.5557
.5948
.633"1
.6700
.7054
.7389
.7704 I
.7995
.8264
.8508
.8729
.8925
.9099
.925"1
--~~2
.9495
.9591
.9671
.9738
.9793
.9838
.9875
.9904
.9927
.9945
.9959
.9969
.9977
.9984
.9988
.9992
.9994
.9996
.9997
.05
.5199
.5596
.5987
.6368
.6736 ...
.7088
.7422
.7734
.8023
.8289
.8531
.8749
.8944
.9115
.9265
.9394.. -
.9505
.9599
.9678
.9744
.9798
.9842
.9878
.9906
.9929
.9946
.9960
.9970
.9978
.9984
.9989
.9992
.9994
.9996
.9997
.06
.5239
.5636
.6026
.6406
.6772
.7123
.7454
.7764
.8051
.8315
.8554
.8770
.8962
.9131
.9279
.9406
.9515
.9608
.9686
.9750
.9803
.9846
.9881
.9909
.9931
.9948
.9961
.997'1
.9979
.9985
.9989
.9992
.9994
.9996
.9997
.07
.08
.5279 .5319
.5675 _57·14
.6064 .6103
.6443 .6480
.6-·8-0-8
.7157
.6844
.7190
.7486 .7517
.7794 -.7823
.8078 .8106
.8340 .8365
.8577 .8599
.8790 .8810
.8980 .8997
.9147 .9162
.9292 .9306
.9418 .9429
.9525 .9535
.9616 .9625
.9693 .9699
.9756 .9761
.9808 .9812
.9850 .9854
.9884 .9887
.9911 .9913
.9932 .9934
.9949 .9951
.99..6.. 2-·- ·-.-9963
.9972 .9973
.9979 .9980
.9985 .9986
.9989 .9990
.9992 .9993
.9995 .9995
.9995 .9996
.9997 .9997
.09
.5359
.5753
.6141
.6517
.6879
.7224
.7549
.7852
.8133
.8389
.8621
.8830
_90·15
.9177
.93"19
.9441
.9545
.9633
.9706
.9767
.9817
.9857
.9890
.9916
.9936
.9952
.9964
.9974
.9981
.9986
.9990
.9993
.9995
.9997
.9998