2015/2016 SEMESTER 2 SEMESTRAL EXAMINATION

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1 05/06 SEMESTER SEMESTRA EXAMINATION Course : Diplom i Electroics, Computer & Commuictios Egieerig Diplom i Aerospce Systems & Mgemet Diplom i Electricl Egieerig with Eco-Desig Diplom i Mechtroics Egieerig Diplom i Mufcturig Egieerig Diplom i Digitl & Precisio Egieerig Diplom i Aerouticl & Aerospce Techology Diplom i Biomedicl Egieerig Diplom i Notechology & Mterils Sciece Diplom i Egieerig with Busiess Module : EG008 / EG96 / EG96 EGB07 / EGC07 EGD07 / EGF07 EGH07 / EGJ07 / EGM07 Egieerig Mthemtics B Egieerig Mthemtics B Egieerig Mthemtics B Mthemtics B Feb/Mr 06 Time Allowed: hrs INSTRUCTIONS TO CANDIDATES This emitio pper cosists of Fourtee (4) pges icludig this pge. This emitio pper cotis sectios. Sectio A: Sectio B: 6 Questios Questios 3 Aswer A questios i Sectio A d Sectio B. 4 All workigs d presettios must be show clerly. 5 Begi ech questio o ew pge of the swer booklet. 6 Mthemticl formul tbles re provided from pge 9 to 4 of this pper.

2 Semestrl Em / EG008, EG96, EG96, EGB07, EGC07, EGD07, EGF07, EGH07, EGJ07, EGM07 / Pge SECTION A - ANSWER A QUESTIONS ( 60 Mrks ) Questio The begiig slries (i thousds of dollrs) of smple of 0 polytechic grdutes i 04 re s follow: Slry (i thousds of dollrs) Frequecy (i) Copy d complete the frequecy tble show bove. ( 3 mrks ) (ii) Fid the me d the stdrd devitio of this smple. ( 4 mrks ) (iii) Fid the mode d the medi of this smple. ( 3 mrks ) Questio () (b) A compy wishes to promote the sles of its brekfst cerel. The compy puts toy i /3 of brekfst cerel boes sold globlly. Joseph wishes to collect the figurie, so he bought 5 boes of the cerel. Fid the probbility tht he will collect the toy. ( 5 mrks ) Globlly, verge of 3 cses of disese is reported every 0 yers. (i) (ii) Fid the probbility tht there re ectly 3 reports of the disese i the et 0 yers. ( mrks ) Fid the probbility tht there is o report of the disese i the et yer. ( 3 mrks )

3 Semestrl Em / EG008, EG96, EG96, EGB07, EGC07, EGD07, EGF07, EGH07, EGJ07, EGM07 / Pge 3 Questio 3 A estte mgemet compy wts to study the reltioship betwee the mothly electricl cost (y dollrs) of house d the verge outside temperture ( degree Celsius). A smple of 0 households ws surveyed. The sctter digrm d the Ecel summry output re show below: SUMMARY OUTPUT Regressio Sttistics Coefficiets Stdrd Error Multiple R Itercept R Squre X vrible Adjusted R Squre Stdrd Error Observtios 0 () Stte the correltio coefficiet d commet o the reltioship betwee the mothly electricity cost (y) d the verge outside temperture (). ( 4 mrks ) (b) Fid the equtio of the best fit lie, y b. Iterpret the physicl sigificce of the vlue of. ( 3 mrks ) (c) Usig your swer i (b), estimte the mothly electricl cost if the verge outside temperture is 5 degree Celsius. Is this estimte relible? ( 3 mrks )

4 Semestrl Em / EG008, EG96, EG96, EGB07, EGC07, EGD07, EGF07, EGH07, EGJ07, EGM07 / Pge 4 Questio 4 A studet coducted survey o smple of 000 dults to fid out whether they smoke d if they hve lug problem. et S deote the evet tht the dult smokes, d deote the evet tht the dult hs lug problem. A summry of his fidigs is s follows: Hs ug Problem, No ug Problem, Smokes, S 93 7 Does ot smoke, S (i) Fid the probbility tht rdomly selected dult does ot smoke d hs o lug problem. ( mrks ) (ii) Fid the vlue of P( S). ( 3 mrks ) (iii) Fid the vlue of P S. ( 3 mrks ) (iv) If two dults re selected t rdom, fid the probbility tht both dults do ot smoke. ( mrks ) Questio 5 () Suppose we hve the letters A, W, X, Y, Z. (i) (ii) Fid the umber of 3letter words tht c be formed without repetitio. ( mrks ) Fid the umber of wys we c rrge ll the 5 letters, without repetitio, if the first letter must be W. ( mrks ) (b) I club there re 8 boys d 4 girls. How my wys c sub-committee of 5 be formed if: (i) there is o restrictio, ( mrks ) (ii) there re more boys th girls d this sub-committee must hve t lest oe girl. ( 4 mrks )

5 Semestrl Em / EG008, EG96, EG96, EGB07, EGC07, EGD07, EGF07, EGH07, EGJ07, EGM07 / Pge 5 Questio 6 () Fid the sum of ll positive itegers betwee d 05 (iclusive) tht re multiples of 5. ( 5 mrks ) (b) A geometric sequece is give by It is give tht k 0. k 3 4, k, k,,... (i) Stte the first term d the commo rtio. ( mrks ) (ii) Show tht the sum of the first terms is 8 k, k where is odd iteger. ( mrks ) (iii) Suggest vlue of k for the sum to ifiity to eist. ( mrk ) END OF SECTION A

6 Semestrl Em / EG008, EG96, EG96, EGB07, EGC07, EGD07, EGF07, EGH07, EGJ07, EGM07 / Pge 6 SECTION B ANSWER A QUESTIONS ( 40 mrks ) Questio 7 () The size of eggs produced by Suyside Egg Frm is ormlly distributed with me of 60 g d stdrd devitio of 5 g eggs re produced ech dy d the eggs re grded s follows: Grde Mss of ech egg, X (i grms) Premium X 68 Norml 56 X 68 (i) (ii) (iii) Fid the probbility tht rdomly chose egg is of Norml grde. ( 4 mrks ) Fid the epected umber of eggs of Norml grde the frm c produce ech dy. ( mrks ) Premium eggs re pcked i trys of 0 eggs ech d ech try is sold t price of $. Wht is the epected dily reveue the frm c er from the sles of Premium eggs? ( 4 mrks ) (b) The life sp of the bttery pcks re kow to be ormlly distributed with me of 50 hours d stdrd devitio of 0 hours. Four bttery pcks re selected from the compy, wht is the probbility tht the verge lifetime of these four pcks is more th 60 hours? ( 4 mrks ) (c) The test redigs (i mg/dl) of blood clcium level is tke from te ptiets. Assume tht the totl blood clcium level is ormlly distributed (i) (ii) Usig clcultor, fid the smple me d the smple stdrd devitio s. ( mrks ) Fid 99% cofidece itervl for the popultio me of the totl clcium level i the blood. ( 4 mrks )

7 Semestrl Em / EG008, EG96, EG96, EGB07, EGC07, EGD07, EGF07, EGH07, EGJ07, EGM07 / Pge 7 Questio 8 () Usig itegrtio by prts, evlute (b) A periodic fuctio f t is defied by 3 t f t for t 3 si t dt, where is costt. t d f t f t ( 6 mrks ) (i) Stte whether the periodic fuctio is eve or odd. ( mrk ) (ii) Fid the Fourier coefficiets 0, d b. ( 7 mrks ) (iii) Write dow the first three o-zero terms of the Fourier Series for f t. ( 3 mrks ) (iv) Plot the Amplitude Spectrum for f t up to the third hrmoic. ( 3 mrks ) END OF SECTION B

8 Semestrl Em / EG008, EG96, EG96, EGB07, EGC07, EGD07, EGF07, EGH07, EGJ07, EGM07 / Pge 8 THIS PAGE IS INTENTIONAY EFT BANK

9 Semestrl Em / EG008, EG96, EG96, EGB07, EGC07, EGD07, EGF07, EGH07, EGJ07, EGM07 / Pge 9 Formul Tbles Rules o Differetitio/Itegrtio Product Rule: d du dv uv v u, u, v re fuctios of Quotiet Rule: du dv v u d u v v d d du Chi Rule: f u f u du Itegrtio by Prts: u dv uv vdu fg gf Specil Cse: fg, m m where f f, g mg Stdrd Derivtives d d d cf c f c = costt d si cos d cos si d t sec d cot csc d csc csc cot d sec sec t d e e d l d cos d d t si Stdrd Itegrls (The costt of itegrtio is omitted) ( ) b b l f l f f si si cos b cos b cos si cos b si b t sec sec b t b sec t sec csc cot sec l sec t csc cot csc ( ) sec l sec t b b b csc l csc cot = l csc cot csc( b) l csc( b) cot( b) or = l csc( b) cot( b) e e b b e e si si t t l

10 Semestrl Em / EG008, EG96, EG96, EGB07, EGC07, EGD07, EGF07, EGH07, EGJ07, EGM07 / Pge 0 Arithmetic Sequece The th term, u d S d Sum of first terms, = first term lst term Me d Vrice of Rdom Vrible The Me of discrete rdom vrible X is k P X k The Vrice of discrete rdom vrible X is k P X k or k P( X k) Geometric Sequece The th term, u r r Sum of first terms, S, r 0 r Sum to ifiity r Mesures of Cetrl Tedecy Smple me: Smple vrice: s or Useful Trigoometric Fcts si si 0 cos cos ier Regressio ie y m C, m is the slope/grdiet d C is the y- itercept Some Useful Trigoometric Idetities si cos t sec cot csc Summtio Properties cos cos si si cos Coutig Permuttio:! Pr r!! k! k!... k! m C C i C C i i i i i yi y i i i i i Biomil Distributio X ~ B, p p where P X C p p, 0,,,..., E X Vr X pq q p Poisso Distributio X ~ P o e P X, 0,,, 3,...! E X Vr X Combitio: Probbility! Cr r! r! PE PE PE P A B P A PB P A B E, E is evet & S smple spce S, E is complemet evet of E Coditiol Probbility P A B PB P A B or P A B P A B PB P A B 0 P A B 0 PA B P A PA B P A P B

11 Semestrl Em / EG008, EG96, EG96, EGB07, EGC07, EGD07, EGF07, EGH07, EGJ07, EGM07 / Pge Fourier Series The Fourier series for periodic fuctio f t with period is: t t f t 0 cos bsi where the Fourier coefficiets re give by: 0 f t dt t f ( t)cos dt (,, 3,...) t b f ( t)si dt (,, 3,...) Cofidece Itervl for Popultio Me, Popultio Vrice, Smple size, Cofidece Itervl, c zc Kow Ay, zc zcs Ukow 30, tcs Ukow 30, zcs tcs

12 Semestrl Em / EG008, EG96, EG96, EGB07, EGC07, EGD07, EGF07, EGH07, EGJ07, EGM07 / Pge Tble : Stdrd Norml Distributio 0 z z z

13 Semestrl Em / EG008, EG96, EG96, EGB07, EGC07, EGD07, EGF07, EGH07, EGJ07, EGM07 / Pge 3 z 0 z z

14 Semestrl Em / EG008, EG96, EG96, EGB07, EGC07, EGD07, EGF07, EGH07, EGJ07, EGM07 / Pge 4 Tble : t Distributio t t t t t t t t t t evel of cofidece, c Oe til, d.f. Two tils, END OF PAPER