POLYTECHNIC OF NAMIBIA SCHOOL OF HEALTH AND APPLIED SCIENCES DEPARTMENT of MATHEMATICS AND STATISTICS

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1 POLYTECHNC OF NAMBA SCHOOL OF HEALTH AND APPLED SCENCES DEPARTMENT of MATHEMATCS AND STATSTCS QUALFCATONS: 1. BACHELOR OF NFORMATON TECHNOLOGY (Business Computing) 2. BACHELOR OF NFORMATON TECHNOLOGY (Software Development) COURSE NAME: COURSE CODE: APPLED STATSTCS & PROBABLTES for T ASP61 OS DATE: DURATON: MARKS: JUNE HOURS 100 1st OPPORTUNTY EXAMNATON PAPER EXAMNER: MODERATOR: MR. ROUX, A.J DR. AJBOLA, KO NSTRUCTONS: a. Answer all the questions in the booklet provided b. Show clearly all the steps used in the calculations c. All written work MUST be done in blue or black ink and sketches must be done in pencils. PERMSSABLE MATERAL 1. Calculator APPENDX: 1) Formulae Sheet 2) Statistical Tables This ー セ j consist of 6 pages including this cover 1

2 ' QUESTON 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 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 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) nterval [2] 1.5 Researchers do sampling because of all of the following reasons except a) Reduce cost b) Can be done in a shorter time frame c) Sampling is interesting d) Easy to manage due to manageable logistics requirements [2] 1.6 Event A and B are said to be collectively exhaustive in statistics if a) A and B are mutually exclusive b) The union of A and B equals the sample space c) The union of A and B is an empty set d) The intersection of A and B is the same as the union [2] 2

3 1. 7 Which of the following is NOT a possible probability 65 a)- 1oo b) 1.16 c) 0 d) All of the above [2] 1.8 A student is chosen at random from a class of28 girls and 12 boys. What is the probability that the student is NOT a boy 3 a)- 10 b) c) 28 d) [2] 1.9 On a multiple choice test, each question has 4 possible answers. f you make a random guess on the first question, what is the probability that you are correct a) 4 b) 0 c)0.25 d) 100 [2] 1.10 A 6-sided die is rolled. What is the probability of rolling a 3 or a 6 a) 12 b)! 6 1 c)- 3 d) 0 [2] QUESTON 2 [101 The data below shows scores in ASP61 OS for a random sample of 7 students in a class test. 86, 72, 23, 56, 62, 94, 48 Use the data provided to find the following: 2.1 The average score a) 64 b) The modal scores a) 86 b) no mode 2.3 The median scores c) 100 c) 23 [1] [1] a) 72 b) 62 c) no median [2] 3

4 2.4 The range of the scores a) 72 b) The first quartile of the scores a) 62 b) The third quartile of the scores a) 88 b) The inter-quartile range for the scores a) 0 b)38 c) 38 c) 71 c) 62 c)17 [2] [1] [2] [2] [1] QUESTON 3 [15] A switchboard operator receives on average 6 calls per minute. What is the probability that for the next minute: 3.1) No calls will be received 3.2) Exactly 4 calls will be received 3.3) At least three calls will be received [4] [4] [7] Question 4 [15] t is known that 90% of drivers are wearing seat belts. Thus, in a random sample of 25 drivers, what is the probability that: 4.1) Exactly 20 of them will wear their seat belts 4.2) At least twenty of them will wear their seat belts 4.3) At most twenty four of them will wear their seat belts [3] [6] [6] 4

5 エ ャZ suitable critical value for the decision rule (3) a) ± b) ± c) ± d) None of the above 3.4) Compute the sample statistic (3) a) M b) M c) d) None of the above 3.5) What is the decision (3) a) Reject Ho b) Do not reject H o... /,/ c) None of above, ''' J lrnn..cun that 90% of drivers are wearing seat belts. Thus, in a random sample o s, what is the probability that: エウッセエセMセNセM キ ゥANAスyセイオZ@ 4.1) Exactly 20 of them will wear their seat belts ) At least twenty of them will wear their seat belts スSZTGM@twenty four of!jle!!!..th.e.ir...s.eat.belts... セᄋM ᄋM セ M QUESTON 5 [10] A factory production line is manufacturing bolts using three machines, A, B and C. Of the total output, machine A is responsible for 25%, machine B for 35% and machine C for the rest. t is known from previous experience with the machines that 5o/o of the output from machine A is defective, 4% from machine Band 2% from machine C. 5.1) What is the probability that a randomly selected bolt is defective? [7] 5

6 G 5.2) A bolt is chosen at random from the production line and found to be defective. What is the probability that it came from machine B? [3] QUESTON 6 [301 The daily study time for high school learners for the coming final examination period can be approximated by a normal distribution with a mean time of 100 minutes per day, and a standard deviation of 1 0 minutes. 6.1) Determine the probability that the maximum daily study time will be between 100 minutes and 125 minutes ( 5) 6.2) Determine the probability that the maximum daily study time will be between 94 minutes and 108 minutes (8) 6.3) Determine the probability that a given day's maximum study time will be exceed 87 minutes (5) 6.4) A chief electrical engineer at a small coal driven power station has accumulated the following information on quarterly electricity generation at his plant (in MegaWatts): セNセA]セpセエp セMゥオj@ ' : 2007 i 2008 Jan-Mar M Oct-Dec M セ M セ M Find the typical median seasonal indexes (12) Xxxxxxxxxxxxxxxxxxxxxx END OF EXAMNATON PAPER xxxxxxxxxxxxxxxxxx 6

7 STATSTCAL FORMULAE SHEETS & TABLES APPENDX A: Formulae Sheet APPENDX B: Additional Formulae Sheet APPENDX C: The Standard Normal Distribution APPENDX D: Areas in the tail of the Standard Normal Distribution APPENDX E: The t-distribution APPENDX F: The Chi-Square Distribution

8 APPENDX A Population mean, raw data Sample standard deviation, raw data _EX2 - CVCJ2 セ S = '\ -1 Sample mean, raw data Sample standarddeviation, grouped data n Weighted mean Coefficient of variation CV= s X {loo) Geometric mean Location of percentile p Lp = (n+l) 100 Geometric mean rate of increase Pearson' s Correlation coefficient GM Value at end of period Value at start of period r = n (l:xy) - (}:X) (l: Y) Sample mean grouped data X = }:fx n Correlation test of hypothesis t = Median of grouped data T -CF Median = L + f Mean deviation "' X-X MD = LJ n (Class width) Population standard deviation for raw data ". r.cx <'l' Population variance for raw data az = E<X- N f.. L)2 Linear regression equation Y = a+ qx Slope of regression line b = n (l:xy) - {2:X) (2:Y) Sample variance for raw data n-1 ntercept of a regression line a 2:Y --b ( r:) n Sample variance, raw data computational form The Range g2 = ;X2 - <Dt>z n n-1 Range highest - lowest

9 APPENDX B: ADDTONAL FORMULAE Mode = L + ( d 1 J x c dl +dz.. Q jn position 1 = - 4 value.. p jn position,. = value jn -F))xc ( P. = L +...:_1_0_0 :; 1 fpj P(AB)= P(AnB) P(B) X-J.l z=-- a zcalc ] O X-J.l zcalc = xi -Xz sz sz _1 +_l xi-xz (calc = ---;================(===J (n + (n -1)si! +! K セョ R MQ@ n 2 p-:c z=--==== Z ャH イゥセ@ ir) q =1- p r = (1 + i)m -1 D = B(l-iY P= A (l+if PV = P(1+if (1+ JY

10 jo.2967 APPENDX C: The Standard Normal Distribution z o.oo 1 o.o1 o.o2 o.o o.o 1 o.oooo 1 o.oo4o 1 o.oo8o 1 o.o 120 jo.0160 jo jo o.o319 lo.o jo.0398 jo.0438 lo.0478_ jo.0517 _ jo.o557.. _, jo.o636 jo.0675 jo.o714 jo.o lo.0793 jo.o832 lo.0871 _jo.0910 jo.0948 jo.o987 jo.1o26 jo.064 jo.1103 jo.1141 o.3 lo.1179!o.1211 lo.255 lo jo lo o.48o lo.1517 o.4 1 o o.591 lo.628 lo o.11oo jo.1112 jo.808 lo.844-jo o ェッ N セ PQY@ jo.2054 _ lo TRSRN ッQ セRNッャMWュ Nd ヲMVN jo.2389 lo jo.2486 lo.2517 lo o.1 lo.258o jo.26u jo.2642 lo jo.2734 lo.2764 lo o QセNRYSY@ u QセNRYU@ ャッセSQPV@ o.8 jo.2881 jo.2910 _ jo o.9 f joj186 _lo.3212 loj238 joj jo.3340 loj r 1.0 loj413 loj438 jo.3461 loj485 loj jo.3554 jo oj599 loj loj jo.3770 joj790 r----rm loj849 joj869!o.3888 lo.3907 lo lo lo.4015 ェッNセSUW@ Q PNセSYT M o.4o49 1 o.4o66 1 o fo ! o f0ai92-lo.4207 lo.4222 jo jo jo.4306 ioa3i9-1.5 'jo.4332 lo.4345 lo lo lo joa452 jo.4463 jo.4474 lo.4484 lo.4495 lo.4505 lo.4515 lo jo lo.4554 jo.4564 jo.4573 lo.4582 lo.4591 lo.4599 lo o lo.4641 lo.4649 lo.4656 jo lo.4713 jo.4719.,0.4726!o.4732 lo.4738 jo.4744 r--lo.-47-5o-r--jo lr--o o ! 2.0 jo.4772 lo.4778 lo.4783 lo.4788 lo.4793 lo.4798 lo.4803 lo.4808 jo.4812 ro lo.4826 jo lr--o.-48_3_8 M イセ PMNTMXTMRMQPNTXTV@ {oa [ 2.2 f0as61-lo.4864 jo.4868 joasn-lo.4875 lo jo.-48_8_1 -r-lo-.4-88_4_!o.4887 jo.4890 j! 2.3 lo.4893 joa896 lo.4898 io.4901 l.-o o_.4_9_06-o.4909 j jo.4913 fo.4916-l セ NTYQX@ lo.4920 lo.4922 jo.4925 lo.4927 jo.4929 r--lo.-49_3_1 -r-jo-.4-93_2_1r--o j o.494o [OA UTYセNッ@ _? _ 1 PVYTNセ@ joa965 [OA966 lo.4967 ェッ N セ YVX@ lo.4969 lo.497o lo.4971 lo.49?2 fo.4973 fd jo _7_7 -rlo-_ , イッセ TYXP@ jo.4981 _ 2.9 jo.4981 lo.4982 lo.4982 ャッ N セ YXS@ _.---jo ,_lo rl-o lo.4986 _ lo.4986 j3jl[oa98-7foa987-foa987-o.4988 lo.4988 Q.4989 jo.4989 jo.4989 fo.499o--lo..499o M

11 APPENDX D AREAS N THE TAL OF THE NORMAL DSTRBOTON z ,. '} v..;;.., u ?_,:::>, :

12 APPENDX E : The t-distribution dt\p o.32492o o o _, セ 3 1 o o , _ o , , _, jo267'i" , o o , j i 7 1 o o f r o o _ , o o o o o o , LRNUVセQRNXYXRS@ LQNSQセYWR@ 13 1 o o , o o , f o o , ! o o , , ! o o o r f o o , ! o jo , o , o o , , r, o o _ o o.68485o f o.68443o o o , , r-v , j o o fl ,2.0484_ QRNWVM セ M f f , o f2.457m-12.75ooo l inf 1 o o.67449o , , [ J

13 APPENDX F: The Chi-Square Distribution 1 df\p oo.750.5oo.250.1oo.o5o oo5 ltl o.oooo4 o.ooo16 o.ooo98 o.oo393 o o.o1oo3 1 o.o2o1o 1 o.o5o o QWNSWセWV@ j3jo.o772 jo lo lo jo.s8437! o o foa o.no ! f fs jd jt j2.6746o f" j , , i 1 1 o j tl f [ f o17o4jt o !2o fslt f j7.344i2-j jt o.o j QXNS セ RXS@ r , Jloj , , llll , , fl , , , , , , RYPVNTQ セ@ [ l f6.4o j [ j , QRWN セ UWLSPNQTSUS@ j i jlo f8.2604o fl QRXNTQYXQSQN セ QPTS@ o j4t flll [36.7so11 J4o ! [13.090s oo69o t.6384o f , [ f f , i f28! fs [41.illi : [30! J14: f2d jso j