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**Unformatted text preview: **CONFIDENTIAL CSIMAR 2016/STA108 UNIVERSITI TEKNOLOGI MARA
FINAL EXAMINATION COURSE : STATISTICS AND PROBABILITY
COURSE CODE : STA108 EXAMINATION : MARCH 2016
TIME : 3HOURS INSTRUCTIONS TO CANDIDATES 1. This question paper consists of ﬁve (5) questions. 2. Answer ALL questions in the Answer Booklet. Start each answer on a new page. 3. Do not bring any material into the examination room unless permission is given by the
invigilator. 4. Please check to make sure that this examination pack consists of: i) the Question Paper ii) a three — page Appendix 1
iii) an Answer Booklet — provided by the Faculty
iv) two graph papers — provided by the Faculty 5. Answer ALL questions in English. DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO $0
This examination paper consists of 5 printed pages
© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL CONFIDENTIAL 2 CSIMAR 2016ISTA108 QUESTION 1 a) State the measurement scale used (nominal, ordinal, interval or ratio) for each of the
following variables. i) Length of a frog’s jump.
ii) Number of typing errors in a report.
iii) Students’ grades in an examination. iv) Marital status of employees in AA Enterprise.
(4 marks) b) A researcher wishes to conduct a study on the type of daily newspaper readership based
on race in Bintang Town which consists of 20,000 people. The residents’ breakdown are 60% Malay, 20% Chinese, 15% Indian and 5% others. A random sample of 400 people
will be selected for this study. i) State the population for this study. ii) Determine the variable of interest in this study and state its type. iii) Suggest the most suitable sampling technique that is appropriate for this study. iv) If systematic sampling technique is used, describe the steps on how to select the sample for the Malay race.
(9 marks) QUESTION 2 a) The marks scored obtained by 20 students in their Mathematics examination is shown
below. 40 25 36 14 1 0 38 29 42 8 1 6
22 49 34 22 18 30 1 1 22 40 38 i) Construct a stem-and-leaf diagram for the above data. ii) Find the mode, median and range.
(6 marks) © Hak Cipta Universiti Teknologi MARA CONFIDENTIAL CONFIDENTIAL 3 CS/MAR 2016ISTA1 08 b) A telecommunication company conducts a research on their new data plan for students.
A sample of students from College Gemilang was asked how much they spent monthly
on a cell phone plan. The data is shown as follow: Monthly spending on cell phone plan (RM) Number of students
30 - 39 10
40 - 49 14
50 - 59 26
60 - 69 12
70 - 79 8 i) Find the mean and standard deviation of the monthly cell phone plan spent by
students. ii) Draw an ogive for the above data. iii) Estimate the median using the ogive in (ii) and interpret the value obtained. iv) Calculate the skewness for the monthly cell phone plan distribution. v) The mean and variance of the monthly cell phone plan spent by students from College Tawakal were RM60 and RM100, respectively. Determine which college is
more consistent in its monthly cell phone plan. (17 marks)
QUESTION 3
. 3 2 . 1
a) Given that P(X) = 3’ P(Y | X) = 3 and P(X nY) = 3’ calculate
i) P(Y)
ii) P(X u Y')
iii) P(X'| Y')
(9 marks) b) How many different ways can all the letters in the word ‘HETEROGENEOUS’ be arranged if the vowels have to appear together?
(3 marks) © Hak Cipta Universiti Teknologi MARA CONFIDENTIAL CONFIDENTIAL 4 CSIMAR 2016/STA108 c) B&C Sdn. Bhd. produces two types of radios, 60% are X radio and 40% are Y radio. A
radio is randomly selected from a production line to check if it is malfunction. From the
past data, it is known that 5% of X radios and 3% of Y radios are malfunction. i) Draw a tree diagram for the above situation.
ii) Find the probability of getting a malfunction radio. iii) If a radio was inspected and found to be malfunctioned, what is the probability that it is a Y radio?
(8 marks)
QUESTION 4
a) The random variable X has probability distribution given in the table below
x -2 -1 0 1 2
ng =x) 0.1 0.3 0.2 c 0.1
Find
i) the value of c.
ii) P(X > 0).
iii) cumulative distribution of X.
(8 marks)
b) A continuous random variable X has a probability density function given by:
kx ; 0 s x < 2
f(x)= k(x—1) ; st<4
0 ; elsewhere.
i) Show that the value k =%.
ii) Compute the probability that X is at least 3.
iii) Calculate V(3X - 2).
(16 marks) © Hak Cipta Unlversiti Teknologi MARA CONFIDENTIAL CONFIDENTIAL 5 CSIMAR 2016ISTA108 QUESTION 5 a) The following table list the number of defective(s) 60—watt light bulbs found in samples of
200 bulbs selected over 10 days from a manufacturing process. Defective(s) Defective(s) i) Find the fraction of the defective(s) 60-watt light bulbs for each day. ii) If a control chart is to be constructed, calculate the center line and control limits for
the fraction of the defective(s) 60-watt light bulbs from the manufacturing process. iii) Plot the fraction of the defective(s) 60-watt light bulbs in the control chart in (ii) and
comment on the manufacturing process. (11 marks)
b) The overall length (in cm) of a cigarette lighter used in an automobile application is
monitored using the control limits of mean and range charts. The following are statistics and three sigma control limits obtained from 10 samples, each containing three cigarette
lighters. Xi = 108.75 ZR = 59 Lower ControlLimit= 6.574 Upper ControlLimit = 15.176 i) By assuming the process meets the speciﬁcation, estimate the potential and actual
process capabilities if the specification limits for the above data is 10.500 :l: 1cm. ii) Interpret the values obtained in (i).
(9 marks) END OF QUESTION PAPER © Hak Cipta Universiti Teknologi MARA CONFIDENTIAL CONFIDENTIAL APPENDIX 1 (1) FORMULA LIST Sample Measurements —=_Z: 1. Mean, x or
n
Zr
~ 7 ‘ Zia—1
2. Median, x = Lm + f C 3. Mode, >2 _ L,no + [—A1—J-c
A1 5. Coefﬁcient of Variation, CV = g x 100 CSIMAR 201 GISTA1 08 _ 3 Mean — Median
6. Pearson’s Measure of Skewness = M— or (———l
Standard Devnation Standard Devration
where
n : total frequency ‘
L m : lower median class boundary
L mo : lower modal class boundary
me : cumulative frequencies for the classes before the median class
f m : median class frequency
A1 : (modal class frequency) — (frequency for the class before the
modal class)
A 2 : (modal class frequency) - (frequency for the class after the
modal class)
C : class size © Hak Cipta Unlversitl Teknologi MARA CONFIDENTIAL CONFIDENTIAL APPENDIX 1 (2) CSIMAR 2016ISTA108 FORMULA LIST
Probability Theory 1. Conditional Probability P(A|B) = $351 2. Multiplicative Rule
P(A n B) = P(B).P(A|B) P(A n B) :4 P(A).P(B) if and only if A and B are independent events. 3. Bayes Theorem
P(A).P(B|A) P(AIB) = P(A).P(BIA) + P(A').P(B|A’) e Hak Clpm Universltl Teknologl MARA CONFIDENTIAL CONFIDENTIAL APPENDIX 1 (3) CSIMAR 2016ISTA108 Control Chart Factors for Mean and Range (American Usage) 32—1181 and R charts Obser- RANGES
in 4 -1e CommlLimiIs Central Line Control Limits 2 0.853 0 3.267
3 0.888 O 2.574
4 0.880 0 2.282
5 0.864 O 2. 1 14
6 0.848 0 2.004
7 0.833 0.076 1.924
8 0.820 0.136 1.864
9 0.808 0.184 1.816
10 0.797 0.223 _1 .777
1 1 0.787 0.256 12744
12 0.778 0.283 1.717
13 0.7770 0.307 1.693
14 0.763 0.328 1.672
15 0.756 0.347 1.653
16 0.750 0.363 1.637
17 0.744 0.378 1.622
18 0-739 0391 1.608
19 0.734 0.403 1.597
20 0.729 0.415 1.585
21 0.724 0.425 1.575
22 0.720 0 .434 1,566.
23 0.716 0.443 1.557
24 0.712 0.431 1.548
25 0.708 0.459 1.541
To derive control limits
Process Average A7 Chart Range Chart
Upper Control Limit = Central Line +213 If Upper Control Limit = D4 71
Lower Control Limit = Carma]. Line 412 E Lower Control Limit = D3 17
Central Line = X fortrial limits Central Line = Ta for trial limits
Central Line = Target mean for a controlled process For achievable known prom o; replace F by d; 0-. © Hak Cipta Universiti Teknologi MARA CONFIDENTIAL ...

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