STA108 (2).PDF - CONFIDENTIAL CSIMAR 2016/STA108 UNIVERSITI...

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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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