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GCE JUN 2007 : AS, S2: Statistics2 (Irish Medium)

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ADVANCED General Certificate of Education 2007 Matamaitic Aonad Meas naithe S4 ag meas n Mod l S2: Staitistic 2 [AMS41] D C ADAOIN 20 MEITHEAMH, IARN IN AM 1 uair 30 n im ad. TREOIR D IARRTH IR Scr obh d Uimhir L rionaid agus d Uimhir Iarrth ra ar an Leabhr n Freagra at leis seo. Freagair gach ceann de na hocht gceist. Taispe in go soil ir forbairt ioml n do fhreagra . Ba cheart na freagra a thabhairt ceart go dt 3 fhigi r bhun sacha mura ndeirtear a mhalairt. T cead agat ireamh n grafach n eola och a s id sa ph ip ar seo. EOLAS D IARRTH IR Is 75 an marc ioml n don ph ip ar seo. L ir onn figi ir ar thaobh na l imhe deise de leathanaigh na marcanna at ag dul do gach ceist n do gach cuid de cheist. T c ip den leabhr n Foirml agus T bla Matamaitice leis seo. S os tr d an ph ip ar seo is ln z an nodaireacht logartamach a s idtear it a dtuigtear go bhfuil ln z log e z AMS4S7 2244 LEATHANACH B N AMS4S7 2244 2 [Turn over Freagair gach ceann de na hocht gceist. Taispe in go soil ir forbairt ioml n do fhreagra . Ba cheart freagra a thabhairt ceart go dt fhigi r bhun sacha mura ndeirtear a mhalairt. 1 T sampla randamach de dheichni r mac l inn as pobal d ocht a c ig mac l inn le glacadh ag In on de Faoite. Thug s c duimhir dh dhigit 01 go 85 do gach mac l inn. Ansin, d s id s pac iste scarbhileoige le liosta de dhigit randamacha a dh anamh mar at l irithe in F or 1 th os. Tos idh In on de Faoite ag barr cl an t bla agus l ifidh go cothrom nach lena sampla a fh il. 0 6 9 1 9 5 3 2 1 8 8 7 4 6 1 6 6 2 7 1 0 7 8 7 7 1 9 7 5 7 4 5 8 4 1 6 5 6 5 2 8 0 7 4 9 6 4 8 5 0 8 0 5 3 3 4 0 4 5 7 7 6 7 3 9 3 9 3 0 2 8 8 7 5 4 4 2 6 6 7 1 2 1 2 F or 1 Agus an modh at in s id agat thaispe int go soil ir, faigh c duimhreacha na mac l inn sa sampla. [4] AMS4S7 2244 [Tiontaigh an leathanach 2 T rang an Uasail de Br n i mBliain 10 d reach i ndiaidh a scr duithe ceann t arma a chr ochn . In T bla 1 anseo th os tugtar na marcanna a fuair sampla randamach de dheichni r mac l inn i dTF agus i mB arla agus taispe ntar iad sa scaipl ar id in F or 2. T bla 1 Mac l inn A B C D E F G H I J Marc TF 49 71 80 75 86 43 78 78 64 55 Marc B arla 59 65 74 84 84 86 70 85 71 53 Scaipl ar id B arla ar TF 90 B arla 80 70 60 50 40 50 60 70 80 90 TF F or 2 Is 0.37 an chomh ifeacht chomhghaoil tr iolr m imint do na sonra seo. Is an choncl id a dh anann an tUasal de Br n go bhfuil comhghaol lag deimhneach idir na marcanna TF agus na marcanna B arla. (i) B fh idir nach bhfuil concl id an Uasail de Br n sl n. M nigh cad chuige AMS4S7 2244 4 [3] [Turn over In T bla 2 th os tugtar na tortha de shampla randamach eile de dheichni r mac l inn i dTF agus sa Mhatamaitic. N l an deacracht i gcuid (i) le sonr anseo. T bla 2 Mac l inn K L M N O P Q R S T Marc i dTF (x) 64 78 46 84 60 75 39 72 52 80 Marc sa Mhatamaitic (y) 75 68 71 77 50 47 54 53 40 47 Anseo th os t staitistic achoimre na sonra seo: x = 650 y = 582 x2 = 44386 y2 = 35462 xy = 38125 (ii) Faigh an chomh ifeacht chomhghaoil tr iolr m imint do na sonra seo. (iii) D an tr cht ar an luach a fuarthas i gcuid (ii). [5] [2] I dturgnamh, taifeadadh an t-am, x n im ad, a ghlac sampla randamach de dhaichead m inteoir puzal sudoku a chr ochn . Anseo th os t na staitistic achoimre: x = 408.3 x2 = 4381.51 Glactar leis go bhfuil d ileadh Normalach ar an phobal. (i) R omh meastach n ar athraitheas an phobail. [2] (ii) Faigh eatramh muin ne 90% don mhe n-am leis an phuzal a chr ochn . [5] (iii) Seachas m id an tsampla a athr , c n t-athr a thabharfadh eatramh muin ne n os leithne? [1] AMS4S7 2244 [Tiontaigh an leathanach 4 T l on ollmh r de cheolrianta st r ilte ar a r omhaire ag an Dr. N Ghallch ir le h s id lena seinnteoir MP3. D anann s dl thdhiosca (DD) le h isteacht leo sa charr tr d deich rian a roghn go randamach agus iad a ch ipe il ansin. M s X an athr g randamach an fad, ina n im id, de rian at st r ilte ar an r omhaire , ansin X ~ N (4.2, 1.6). (i) Scr obh an me n agus an t-athraitheas de X10, me nfhad na rianta ar DD. [2] (ii) Faigh an d ch lacht gur l n 4 n im ad a bheidh me nfhad na rianta ar DD a roghn far go randamach. [5] (iii) Abair gur l rianta a chuirtear ar DD. Cad an ifeacht a bheadh aige sin ar do fhreagra ar (ii)? M nigh do fhreagra. [2] Rinneadh turgnamh lena fh il amach cad an c atad n saille a bh i sceall ga a c car ladh ag teochta difri la. (i) Cad an athr g neamhsple ch sa turgnamh seo? Luaigh f th. [2] I dturgnamh eile fuarthas an c atad n saille (y) i gcoibhneas le ti s (ina mm) na sceall g (x). Anseo th os t luachanna achoimre na sonra : x = 244 y = 302 x2 = 3054.3 y2 = 4584.86 xy = 3719.32 n = 20 (ii) Faigh cothrom id aisch imnithe na n- oschearn g do ch atad n na saille ar thi s. (iii) D an meastach n ar mhe nch atad n na saille faoi choinne sceall g dar ti s 12.5 millim adar. [2] (iv) Cad iad na tuiscint , dar leat, ar glacadh leo leis an turgnamh in (ii) a dh anamh? [6] [2] An d ant ir de bhranda irithe spaghetti, t thar san amhras air gur l n an 500 gram at luaite ar an lip ad at chur isteach sna paic id aige. Baineadh sampla randamach de 10 bpaic ad agus anseo th os t mais, ina graim, an spaghetti a bh i ngach ceann acu: 501.8 496.2 498.7 500.6 499.1 496.8 502.1 495.3 495.8 498.6 Ag glacadh leis go bhfuil d ileadh Normalach ann, t st il ag leibh al 5% an bhfuil aon bhonn leis an amhras. [12] AMS4S7 2244 [Turn over 7 T d ileadh Normalach dar me n ar an athr g randamach X. I sampla randamach de 50 breathn de X fuarthas na staitistic achoimre seo th os: x = 1456 x2 = 42440 T st il ag leibh al 5% na hipit is seo a leanas: H0: = 29.5 H1: 29.5 8 [8] D anann Se n ceapair c ise lena gcur i gcoime d in. T d ileadh Normalach dar me n 10 millim adar agus darb athraitheas 1.6 millim adar2 ar thi s an ar in a s ideann s . T d ileadh Normalach dar me n 12 mhillim adar agus darb athraitheas 2.8 millim adar2 ar thi s na c ise. (i) Faigh an me n agus an t-athraitheas de thi s cheapair She in. (D anann Se n a chuid ceapair le c is idir dh shlis chearnacha d ar n.) [3] Leis na ceapair a chur i gcoime d in, gearrann Se n an ceapaire go trasn nach ina dh thriant n, leagann an d leath ar bharr a ch ile agus cuireann i gcoime d n triant nach plaisteach iad. (ii) Scr obh an me n agus an t-athraitheas de chomhthi s na dtriant n ceapaire sula gcuirfidh Se n sa choime d n iad. [2] Is 65 millim adar an ti s at taobh istigh den choime d n. In amanna b onn ar She n an ceapaire a chomhbhr rud beag lena chur sa choime d n. M s m n 10% an comhbhr ar cheapaire n f idir a s id. (iii) Faigh c atad n na gceapair nach f idir a s id. SEO DEIREADH AN SCR DPH IP IR AMS4S7 2244 7 [7] S 3/06 0000 7-041-1 [Turn over

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Additional Info : Gce Mathematics June 2007 Assessment Unit S2 Module S2: Statistics2 (Irish Medium)
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