CORK INSTITUTE OF TECHNOLOGY INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ Semeste Eamatos 009/00 Module Ttle: Busess Mathematcs ad Statstcs Module Code: STAT 6003 School: School of Busess ogamme Ttle: Bachelo of Busess Yea Bachelo of Busess Busess Admstato Yea Hghe Cetfcate Busess (EOD Yea ogamme Code: BBUSS_7_Y BBADM_7_Y BBUSE_6_Y Eteal Eame: Iteal Eames: M. J. Relly M. K. Clly, M. C. Daly, D. S. O Rouke Istuctos: Aswe thee questos. Show all calculatos IN FULL. Do ot wte, daw o udele RED. Wte you class goup ad lectue s ame afte the wod Secto o the fot page of you aswe book(s. Duato: Hous Note to Caddates: lease check the ogamme Ttle ad the Module Ttle to esue that you have eceved the coect eamato pape. If doubt, please cotact a Ivglato.
Q. (a The output ( thousads of toes of two steel compaes ove the last fve yeas s ecoded below: Yea 005 006 007 008 009 Output of Compay A 303 59 665 840 95 Output of Compay B 704 798 875 905 054 ( Fo each of the two compaes, calculate a fed base de umbe fo each of the yeas 005 to 009, usg 005 00. ( Whch compay has pefomed bette betwee 005 ad 009? Gve a easo fo you aswe. (7 maks (b A Fueal Home povdes thee types of fueal sevce, Stadad, MdRage ad Delue. I ecet yeas thee have bee majo chages the pces ad the quattes of the thee types of fueal sevce. These ae show the table below. Type of Sevce ce ( Quatty Sold 007 008 009 007 008 009 Stadad 000 400 750 50 70 75 MdRage 3500 3800 400 40 45 50 Delue 4500 4700 500 0 5 ( Calculate a aasche ce Ide fo 009 wth 007 00 (4 maks ( Calculate a Laspeyes Quatty Ide fo 008 wth 007 00 (4 maks ( Calculate a weghted athmetc mea of pce elatves de fo 009 wth 007 00, usg 008 value (epedtue weghts. (5 maks
Q. The followg table shows the umbe of customes vsted by a sales epesetatve last week ad the umbe of odes secued by hm: Day Numbe of Numbe of customes vsted odes secued (X (Y Moday 5 0 Tuesday 4 5 Wedesday 8 Thusday 6 Fday 0 4 (a Usg the above data, daw a scatte dagam (scattegaph. (4 maks (b Deteme the equato of the least squaes egesso le (le of best ft, oudg the values of a ad b to decmal places. (6 maks (c Estmate how may odes the sales epesetatve would secue o a day o whch he vsted [] 0 customes [] 8 customes ( maks (d lot the egesso le o the scatte dagam. ( maks (e Calculate the coeffcet of coelato ( ad commet o ts value. (6 maks
Q3. (a ( 400,000 s deposted to a savgs accout that eas compoud teest. If o wthdawals ae made fom the accout, t wll have gow to 459,009 afte fou yeas. Calculate the ate of teest pe aum. ( A savgs accout eas compoud teest at.% pe moth. Calculate the equvalet aual ate of teest ( A compay has puchased a ew packagg mache costg 500,000. The mache wll depecate at a ate of.5% pe aum. Calculate what ts book value wll be afte 8 yeas. (7 maks (b At the begg of each yea fo the et fou yeas, a compay teds to depost X to a skg fud. The fud wll ea compoud teest at 0% pe aum. If o wthdawals ae made fom t, thee wll be 50,000 the fud at the ed of the fouth yea. Calculate: ( the value of X ( the total amout of teest that the fud wll ea ove the fou yeas. (6 maks (c O Jauay, 00 a compay boowed 40,000 fom a bak at 5% pe aum compoud teest. The loa must be epad to the bak thee equal epaymets, due o Decembe 3 00, 0 ad 0. Calculate: ( how lage each epaymet wll eed to be ( the amout that the compay wll owe the bak o Decembe 3, 0 afte t has made the secod epaymet. (7 maks
Q4. (a 5% of the people who ete Blly s Baga Shop make a puchase. Foutee people eteed the shop yesteday mog. Fd the pobablty that ( ( oe of them made a puchase; at least thee of them made a puchase. (7 maks (b The legth of tme that customes sped Blly s Baga Shop s appomately omally dstbuted, wth a mea of eght mutes ad a stadad devato of two mutes. Fd the pobablty that a adomly chose custome wll sped ( ( moe tha e mutes the shop; betwee s ad e mutes the shop. (7 maks (c The umbe of people eteg Blly s Baga Shop follows a osso dstbuto, wth a mea of thee people pe hou. Fd the pobablty that the umbe of people eteg the shop betwee.00 pm ad 3.00 pm tomoow wll be 4, 5 o 6. (6 maks Note: e.783 (appo.
Statstcal Fomulae Laspeye s ce Ide: I aasche ce Ide: I pq 0 pq 0 0 pq pq 0 00 00 q po Laspeye s Quatty Ide: I 00 q p o o q p aasche Quatty Ide: I 00 q p Weghted Athmetc Mea of ce Relatves Ide: I o p p 0 w w 00 Least Squaes Le: y ' a + b y a + b y a + b a a y b ( y b y y y a + b y ( Coeffcet of Coelato:
( ( y y y y. d ' ( 6 Compoud Iteest A ( + + + A A ( ( A Amout eset Value Depecato C B ( Auty Fomulae (aymet Iteval Iteest eod + R A ( + R ( Bomal Dstbuto q p C, ( osso Dstbuto p e λ λ λ!. ( Stadad Uts σ Z