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GCE JAN 2011 : AS, S1: Statistics (Irish Medium)

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ADVANCED SUBSIDIARY (AS) General Certificate of Education January 2011 Matamaitic ag meas n Mod l S1: Staitistic 1 AMS11 Aonad Meas naithe S1 [AMS11] D C ADAOIN 26 EAN IR, 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 seacht 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 ln z logez. 6319.02 Freagair gach ceann de na seacht gceist. Taispe in go soil ir forbairt ioml n do fhreagra . Ba cheart freagra a thabhairt ceart go dt 3 fhigi r bhun sacha mura ndeirtear a mhalairt. 1 Tugtar an d ileadh d ch lachta d athr g scoite randamach, X, in T bla 1 anseo th os. T bla 1 x 1 P(X = x) 2 3 0.17 4 5 0.17 0.23 0.18 (i) M nigh go hachomair cad chuige a gcaithfidh P(X = 2) a bheith cothrom le 0.25 [1] (ii) Faigh E(X ). [2] (iii) Faigh Var(X ). [4] T athr g scoite randamach eile, Y, gaolta le X tr d an fhoirmle Y = 2X 3 (iv) Agus na tortha (ii) agus (iii) in s id, faigh E(Y) agus Var(Y). 2 [3] Chuir P l deich gcinn de bhleibeanna pl ir n sneachta. n taith aige, t a fhios aige go bhfuil seans 65% ann go dtiocfaidh bl thanna ar na pl ir n sneachta san earrach. Faigh an d ch lacht: (i) go dtiocfaidh bl thanna ar 7 gcinn go beacht de na pl ir n sneachta san earrach; [3] (ii) go dtiocfaidh bl thanna ar 7 gcinn ar a laghad de na pl ir n sneachta san earrach; [4] (iii) go dtiocfaidh bl thanna ar 7 gcinn ar a mh ad de na pl ir n sneachta san earrach; [3] 6319.02 2 [Turn over 3 T Treasa ag obair ar thionscadal sa rang Socheola ochta. Roghnaigh s sampla de na daoine a th ann go dt cluich sa ph irc peile iti il agus d fhiafraigh s d obh c n aois a bh siad. Rinne an m inteoir histeagram leis na sonra a achoimri . Ba mhaith le Treasa an me n agus an diall caighde nach de na haoiseanna a r omh. Taispe nann T bla 2 an obair at d anta aici go dt seo. T bla 2 Aois (blianta ioml na) Dl s Minic ochta Minic ocht 0 9 3.2 32 10 14 13.2 66 15 19 13.8 20 29 12.3 30 44 10.2 45 74 1.9 (i) Faigh na ceithre mhinic ocht at ar iarraidh. [3] (ii) Faigh an me n agus an diall caighde nach d aois na ndaoine a th ann go dt cluich . [5] 6319.02 3 [Tiontaigh an leathanach 4 T d ileadh Normalach dar me n 55 n im ad agus dar diall caighde nach 10 n im ad ar na hamanna a ghlacann teaghlaigh leis an tsiopad ireacht sheachtaini il a dh anamh san ollmhargadh iti il. Faigh an d ch lacht go nglacann siopad ireacht sheachtaini il teaghlaigh: (i) n os l n 60 n im ad; [3] (ii) idir 45 n im ad agus 60 n im ad. [4] I gc s teaghlaigh irithe, is sa 15% uachtar d amanna siopad ireachta at an t-am a ghlacann siad leis an tsiopad ireacht sheachtaini il a dh anamh. (iii) Faigh an t-am is l a ghlactar le siopad ireacht sheachtaini il an teaghlaigh a dh anamh. 5 [5] T sceitheadh ola i gc rr ine. B onn an ola ag sileadh go randamach faoi mhe nr ta de 16 shilte n in aghaidh an n im id. Agus ag dul go dt an gar iste sa charr, stopann ine ag na soilse tr chta ar feadh 15 shoicind. Agus an carr stoptha ag na soilse, faigh an d ch lacht go silfidh an ola: (i) dh uair go beacht; (ii) 3 huaire ar a laghad. [4] (iii) M shil an ola 3 huaire ar a laghad, faigh an d ch lacht gur shil s s huaire go beacht. 6 [4] [4] Is leis an chothrom id seo th os a shainmh n tear an fheidhm dhl s d ch lachta f(x) d athr g randamach lean nach X f(x) = kxn 0<x<1 an it a bhfuil n > 1 (i) Taispe in go bhfuil k = n + 1 [3] Faigh slonn, i dt arma n, do (ii) E(X ); [3] (iii) Var(X). [5] 6319.02 4 [Turn over 7 [Sa cheist seo s idtear an gn s A leis an teagmhas n A a l iri .] Amharc ar an l ar id crainn d ch lachta seo a leanas. B A x z B y B A B F or 1 In F or 1 thuas is d ch lachta de 3 theagmhas iad x, y agus z. (i) Agus F or 1 in s id, luaigh na teagmhais arb iad x, y agus z na d ch lachta d obh. [3] (ii) Ag glacadh leis go bhfuil z = 1 x agus go bhfuil y = 2x, faigh slonn do P ( B ) i dt arma x. [4] (iii) M t ( B ) = 0.25, faigh x. [5] SEO DEIREADH AN SCR DPH IP IR 6319.02 5 [Tiontaigh an leathanach 6319.02 6 [Turn over 6319.02 7 [Tiontaigh an leathanach 6319.02 6319.02 8 [Turn over

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Additional Info : Gce Mathematics January 2011 Assessment Unit S1 Module S1: Statistics (Irish Medium)
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