MDM 4U MATH OF DATA MANAGEMENT FINAL EXAMINATION

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1 Caadia Iteratioal Matriculatio rogramme Suway Uiversity College MDM 4U MTH OF DT MNGEMENT FINL EXMINTION Date: November 28 th, 2006 Time: 11.30a.m 1.30p.m Legth: 2 HOURS Lecturers: lease circle your teacher s ame. Dzura, Mr. Nithya,. Rohai, Mr. Varga, Mr. Welch Studet Name: Sectio/eriod: lease read the followig istructios carefully before you begi the examiatio: 1. This exam paper has sevetee prited pages, icludig this cover page. 2. The examiatio is worth 30 percet of your fial mark. 3. The examiatio cosists of three parts: RTS, ad C. RTS CONTENT MRKS TIME LLOCTION Multiple Choice MINS Short swer MINS C roblem MINS TOTL The aswers to the Multiple Choice Questios must be writte o page 15 of this booklet. ll other aswers must be writte i the space provided. If you eed more space, cotiue o the blak page to the left of the relevat Questio ad do idicate your itetio. 5. Scietific or graphig calculators are permitted, but NO sharig is allowed. 6. You ca ONLY use the special fuctio of the graphig calculator whe you see the symbol below. Otherwise, use the commo fuctios oly. GC 7. Marks for each questio are idicated iside square brackets, [ ]. 8. Normal Distributio table ad Formula sheet are at the rear of this booklet. For office use oly: art art art C Total FINL EXMINTION/MDM 4U November, 2006 age 1

2 RT Multiple Choice [15 marks] Idetify the letter of the choice that best completes the statemet or aswers the questio. DO REMEMER TO LCE YOUR NSWERS ON GE 15 OF THIS OOKLET 1. Studets at a high school were asked which was their favorite subject. The results are show i the followig graph. Which subject is most popular amog female studets? a. hys-ed c. Sciece b. Music d. Eglish 2. The seior soccer team icludes studets from all grades but most of its members are from the higher grades. The distributio of the ages of team members would likely be a. U-shaped c. right-skewed b. moud-shaped d. left-skewed 3. If X~N15, 4, the 68% of the data fall i the iterval a c b d multi-sided die with less tha 20 sides is rolled. The probability of rollig a umber divisible by 4 is 5 1. The umber of sides of the die must be a. 12 c. 8 b. 10 d Fid the probability that whe a sigle card is draw from a regular deck of cards a diamod or six is chose. a. c. b. d FINL EXMINTION/MDM 4U November, 2006 age 2

3 6. The math club the best club of all! cosists of 10 studets. We must sed a team of three studets to a competitio. How may differet teams are possible? a. 10! c. 3! b. 10,3 d. C10,3 7. studet is preparig a probability distributio as show below. X X value is eeded for 3 to complete the table. Which statemet below is true? a. The required value for 3 is 0.3. b. The required value for 3 is 0.0 c. The required value for 3 is 1 d. There is o possible value for 3 that ca make this a valid probability distributio. 8. Give the matrices below, fid the value of E + 3D. a. c. b. d. 9. The media-media lie a. oly passes through key poits based o medias b. passes through the media x-value ad media y-value of the data c. is aother ame for the lie of best fit d. is used whe there is o correlatio betwee the variables 10. Use the stadard deviatio to determie which of the two baseball teams has bee more cosistet i its scorig for the last five games. New York: 0, 4, 2, 3, 6 St.Louis : 2, 3, 4, 5, 8 a. New York c. They are equally cosistet b. St.Louis d. The result caot be determied FINL EXMINTION/MDM 4U November, 2006 age 3

4 11. artist wis a prize 70% of the time whe she eters a art show. Determie the probability that she will wi exactly oce out of two art shows. a c b d sided die is rolled 4 times. Determie the probability of gettig 3 fives. a. 3 1 c b d uiversity accepts oly applicats scorig i the top 16% o a etrace test. Each year the test scores are ormally distributed with a stadard deviatio of 30. What is the highest value that the mea ca have for Fred to be accepted with a score of 520? a. 460 c. 520 b. 490 d Which of the followig statemets are true? I If has dimesios m x ad has dimesios x p, the the product is defied, ad has dimesios m x p. II If is a 3 x 4 matrix ad is a 3 x 4 matrix, the is defied. III If ad are both defied ad have the same dimesios, the they are equal. a. I oly c. I ad II oly b. II oly d. II ad III oly Geder Mathematics Eglish Males 4 9 Females class is surveyed to determie whether they prefer Mathematics or Eglish. The table above shows the results. Give that a studet is female, state the probability that Eglish is preferred. a. c. b. 8 d FINL EXMINTION/MDM 4U November, 2006 age 4

5 RT Short swer [25 marks] 16. Usig the give equatio for the regressio lie show, determie the amout of time required to completely bur the cadle. [3 marks] 17. The media aual salary of the 6 vice-presidets of VCO Ic. is $ What will this media be if oly the highest paid vice-presidet receives a $ raise? Explai how you derive the aswer. [2 marks] 18. The Swiss embassy i Ottawa has 65 employees. Of these workers, 47 speak Germa, 35 speak Italia, ad 20 speak both Germa ad Italia. Calculate the probability that a employee selected at radom would speak either Germa or Italia? Note: Use the additive priciple for probability theory. [3 marks] FINL EXMINTION/MDM 4U November, 2006 age 5

6 19. For a dace recital, 3 begier groups, 5 itermediate groups, ad 2 advaced groups are to perform. The program is set up so that all the begier groups perform first, the all the itermediate groups, the all the advaced groups. How may differet arragemets are possible? [3 marks] 20. Write the trasitio matrix that represets this digraph. [2 marks] GC 21. Use techology to determie the correlatio coefficiet for the followig set of data. Explai the meaig of this value. x y [3 marks] 22. card is draw from a deck of cards. What is the probability that it is a jack, give that it is a face card? Note: Show the usage of the proper formula [3 marks] FINL EXMINTION/MDM 4U November, 2006 age 6

7 23. The probability distributio for a radom variable X is show below. Determie the expected value of X. robability Distributio for a Radom Variable X robability ossible values for X [3 marks] 24. car retal compay rets four differet types of cars, Ford, Dodge, Hoda, ad Toyota from three differet retal locatios. The compay's retals for March are summarized i the followig table. Locatio Ford Dodge Hoda Toyota I II III The data ca be represeted usig the followig matrix. Suppose that the compay s retals for pril are reduced by 20% of its March figures. Compute the ew matrix. [3 marks] FINL EXMINTION/MDM 4U November, 2006 age 7

8 RT C roblem [60 marks] 25. May books are also made ito movies. survey was take ad people were asked if they would rather read the book first, or watch the movie first. The results are show i the followig table. referece Male Female Read ook First Watch Movie First a Create a split-bar graph to represet these data. b alyze this data & the graph. If you were the ower of a bookstore, what would your marketig strategy be based o this kowledge & uderstadig. Explai your reasoig clearly. [6 marks] FINL EXMINTION/MDM 4U November, 2006 age 8

9 26. pair of dice is rolled several times. The followig scatter plot shows the umber of rolls versus the umber of times a sum of seve occurred. a Draw lie of best fit o the graph. b Idicate o the graph how you would estimate the umber of times a sum of seve would occur i rolls of the dice c If I were to claim that I rolled a sum of seve for 300 times, how may times have I actually tossed dice [hit: utilize iterpolatio of the graph]? [6 marks] FINL EXMINTION/MDM 4U November, 2006 age 9

10 27. The distributio of marks i Mr. Dee s class is always moud-shaped. However, o the last test, most of Mr. Dee s studets received a mark of approximately 70 out of 100. He oticed that 5 studets failed i.e. a mark less tha 50 while oly 2 studets had marks over 90. Why was he surprised? Explai. [4 marks] 28. oth aro ad Marie, who atteded differet schools, fiished grade 12 with fial averages of 82. The mea of these averages i aro s school was 65 ad the stadard deviatio was 10. I Marie s school, the mea was 68 ad the stadard deviatio was 8. a Use z-scores to determie who had the better mark. b James graduated from aother school with a average mark of 89%. He discovered that his mark is oly as good as Marie s mark. Kowig that his school s stadard deviatio is 8, what is his school s average mark? [6 marks] FINL EXMINTION/MDM 4U November, 2006 age 10

11 29. survey of televisio viewers at Child s lace reschool produces the followig data: 60 % watch Sesame Street 50 % watch Captai Kagaroo 50 % watch olka Dot Door 30 % watch Sesame Street ad Captai Kagaroo 20 % watch Captai Kagaroo ad olka Dot Door 30 % watch Sesame Street ad olka Dot Door 10 % watch all three shows a Costruct a Ve Diagram for this data. b What percetage views at least two of the shows? c What percetage views oe of the shows? d What percetage view Sesame Street ad Captai Kagaroo but ot olka Dot Door? e What percetage views exactly two of these programs? [7 marks] FINL EXMINTION/MDM 4U November, 2006 age 11

12 30. Whe Taufiq plays badmito, 56% of his first serves go ito the correct area of the court. If the first serve goes ito the correct area, his chace of wiig the poit is 92%. If his first serve does ot go to the correct area, his chace of losig the poit is 34%. a Draw a tree diagram to represet this iformatio. b Usig the tree diagram, fid the probability that Taufiq loses the poit. c Fid the probability that Taufiq s first serve wet ito the correct area, give that he loses the poit. [9 marks] FINL EXMINTION/MDM 4U November, 2006 age 12

13 31. The followig table gives the sales data from the Kool Hockey Fashio compay for the first four moths of the year i Fashio Item Jauary February March pril ats Jackets T-shirts a Which of the three items of clothig geerated the most umber of sales over the fourmoth iterval? Justify your aswer. b Suppose that ats sell for $20, jackets for $30, ad T-shirts for $10. Use matrix methods to calculate the reveue of the compay for each of the respective moths. c The compay offers two types of promotioal gifts for each item sold durig the respective moths. The quatity of gifts distributed is based upo the followig table: romotioal Gift Jauary February March pril e/s ag/s i Set up the matrix multiplicatio that would produce the total umber over four moths of the respective gifts distributed correspodig to each type of fashio item that was sold. GC ii Use the set-up matrix to ivestigate which of the fashio item resulted i the most umber of bags to be give away. [9 marks] FINL EXMINTION/MDM 4U November, 2006 age 13

14 32. bag cotais 2 red, 4 gree, ad 5 yellow marbles. Three marbles are selected radomly without replacemet. a Create a probability distributio for the umber of red marbles selected. b Determie the expected umber of red marbles selected. c Determie the probability that at least 1 red marble will be selected [6 marks] 33. Determie the umber of arragemets of the letters i MLYSI if a all letters are used. b three letters are used 34. Studies have show that 40% of studets skip oe or more classes per semester. If 5 CIM studets are radomly selected a what is the probability that at least 1 studet has skipped classes? [4 marks] b what is the expected umber of studets to have skipped classes? [3 marks] ***** END OF ER **** FINL EXMINTION/MDM 4U November, 2006 age 14

15 CIM MTHEMTICS OF DT MNGEMENT MDM 4U MULTILE CHOICE NSWER SHEET NME : ERIOD : swer all multiple choice questios o this sheet FINL EXMINTION/MDM 4U November, 2006 age 15

16 FINL EXMINTION/MDM 4U November, 2006 age 16 FORMUL SHEET Chapter 3 Normal Dist. s x x z or σ x µ z S ' 1 + or + or!!, r r! r! r! r Chapter 4 robability! x 1 x 2 x x 3 x 2 x 1 Ε x x xp X C r + C r+1 +1 C r+1 t r+1 r r b a r Chapter 5 robability Distributio x x q p x x X p X Ε