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euaKCS Khau kidm aa ctrft lrrong sdn phdm, rrlor linh kien dat ri€u chutn dugc ch{p nhln vdi ?.. LO tht hai chria6 sen phCrn loai I vi 4 sin phdm loai II.. Ldy ngtu nhien ti]mdi 16 I san

C6u 1: Mot nhi' lody sar suit linh ki€n dien trl vdi tl lQ sln phdm rar deu chudn D 80% eua

KCS (Khau kidm aa ctrft lrrong sdn phdm), rrlor linh kien dat ri€u chutn dugc ch{p nhln vdi

?) T!!! d 16li!!h lder d?t de'r.h'rdn sa'.t KC-s !0,V

neu tE lu;41.

" \ n - L * - - - d Lb) Qtran sdr ngau nhiCd 4 c6n trung, tlnh xtc sudt chl c6 2 coo sdog qua 2 thrdg

c) H6i trung blnh Dhii quan sdt nlSu nhi€n md'y con c6n trDng ttd sau hai th6og aung

(Xein riec quan 6dt c6n trdng Ia doc lep nhau)

Q!g!: Dd nghi€o crlu sd enh hudng cla phan b6n (X) rtdn ning su{r lta (y), 4gddi ra ti6'n baDh

thl ngbiem tren i00 mdnh nrgng vi

thu dfgc kgt que nhu sau :

a), U-dc irJdng trang suai iUa

trung birh hCn mor rtrenh ruotrg

vdi d0 ttu cay 95%

, b), N6u n6i rlng d le neoh

ruong dat neng suft tU l50kg

(

I

' quan tuydn tinh giiia ni;g su{t lrta vdi ludng phan b6n,

(Gie thiei Y c6 pMn phdi chua'd)

6hi chrl : B{ng tra cdn thidt cho phla sau dd rhi

Ngay 29 thdng 05 ndm 2004

BO MdN DUYFT,

I

Cau I C6 h:li Id hrint L6 ihf nhdt chdh 5 sin phdm loai I vir 3 sin chdm loai U LO tht hai chria

6 sen phCrn loai I vi 4 sin phdm loai II Ldy ngtu nhien ti]mdi 16 I san phdm.

a) Tinh xdc sudt dd lI) dudc 2 sln phdm ciurg loai.

b) 86 2 salr phir (r; lai dudc veo ld l, rdi ldy ngau nhien 2 sin phem tt ld nty Tini xdc

*

suri lav duoc 2 sin oh;im khdc loai.

c) Bi6r trong cdc sin pidm ta'y ra cO it nrrait I san phCm loai l Tirlh ric sual dd lty dr,oc siin

-

phdm loai I crla 16II.

d) Coi ]( l;r so sin fhlim lcq.r I trong 2 sin phdm ljy ra Tinh ki vgng var phudnS sai cia X.

( t I - )

- - 8 <

Cau II Krdrn F3ludi tho cua mdt sd bdng den dc nh} mdy A sin xudt ta thu duoc barg sS li€'J

D,lI HOC SIJ PHAM K.t THUAT TP HCM

KHOA KHOA HQC CO BAN

56 b6ng

Biei tuiii tho b6ng den c6 phan phaii chudn.

a) Hay tim khoeng hn ci), cia tLrdi tho trunt binh cia cic b6rg ddn do nhtr mey A san xua't ,si da tin 1y 95q

b) Voi mfc y nghir 37o, dq a vio s6 fieu da ihu duoc, c6 thC ke't luan rudi thq trung binh cria cdc b6n8 dbn do nhe' m6y A sen xutt le 5700 gid hay kl6ng?

c) Hey tim khoing tin cay cira ti le bdng din c6 tudi tho tren 5796 8id voi d6 tin cay 987 d) Vdi muc i rghia 17., dlra veo sd lieu dA (hu dudc, c6 thC kgt luan t:i l€ b6ng ddn c6 tutii tho dndi 558C gid h 10qo hay khong?

2,3 cr.48928 0.489560.,14983 0.490100,49036 1r,4906i 0,19086 0 + l il i 0 4 9 t 3 4 0.!t9l5E

0,49379 0.493q6 0.49411 0,49430 0.49,46 0.49461 0,49477 0 i9491 0_49506 t95ZO

C6u 1 : Cho 3 16 linh kiQn A,B,C g6m rA't nhi6u linh ki€n, tl 16 linh ki€n h6ng 3 m6i 16

Un lwt h 0J; 0p8; q05

a) Til 16 A chgn ra 3 linh kien Tinh xrc sudt duqc thi6u nlqAfinh kien tdt

b) cii s'! m6t llgrrni ddn nna ngiu nhi€n I li kien ti mot cia hang b[n l-gglj linh ki€n Sdrn: 500linh.IiQn 1,hrr6c lJ A 300 thudc ]6 B 200 Lhu6c lo C Tinh

hoc m6i ngiy cria sinh

( 1

\ q l o a l v ) ! ' l "'

b) Tinh d te c6ng rring cd luiii tha chua d&-2 tbdng rudi ron8 sd cdi' trDng c6ru6j $Q r l $5nc trd l6n.

K!,)

t1 /'

r

Da, N* t+;

)LiC SUAT vi THONG K8 TOAN - A

Q!g-! : M6r cfa hing bdy bdn l0 sen phdm cung loai t ong d6 cd 6 sin phdm do td I sen xuai va 4 s6!

ir) i'ilir xic sut't tid cho uong 2 sdn phdm ma krnch mua ngdy hom sau c6 it nhat I san phdm do

b) Vdi a, b tim dudc, &rh tudi rho rrung btnh crla loai bdng dien trCn

d a v :

I not ulem

a), Hiy so sdnh ti i6 16 hdng ddng g6i s6n bi can thidu d 2 rhdi didm tr€n vdi mBc j nghia cr=0,O5

r)hiCu 16 heng ?

nglliti ta kidm trr m6r sd sdn pham thep lam r a v d hu drJdc sd sdn ohdm s6 lieu sau dev :

(gid thidt rlng dQ bdn cria th6p li mot bidn ngau nhien cd phan ph6i chudn)a) Hdy cho k€i luin vC hieu qua c aviecceiridnc6chluyOnrhepvdimfcynghiaCt'=0,01.b) Hay ddc ludng d0 bdn rung binh c0a thdp sau c6i tidn vdi dO tin c6y 95Va

Chi chti : Khong sB dung tdi he'r khi lem bii Bdng tra cin thidt cho phia sau d0 thi

DAI HQC SIJ PHAM KYTHUAT TI.HCM

CAu 1 : Mfl tr+m ctru hda o vitng A c6 3 xe chrra chiy, vi sd cuoc goi cdn ddn su girip

d0 cia xe chna chdy crla ram la bidn nge0 nhien uAn theo lual phir ph6'i Poisson

vdj lham sd ld 1,8 Giri rhidt ring m6L \e chi dip rlng d;oc 0l cu,ic gor rrong m6r

'rgr v

a) Quao sit ngiu nhien m6t ngAy tai tram, tinh xdc sud't dd ngiy ,16 khdng c{i xe nio

phei dem ra drlng.

b) Tinh xdc sutt trong 02 ngey liin ridp rram dirng nhidu nhei 02 xe.

c) Ti le cdc ngiy c6 cu6c goi md lram ki6ng thd ddp r?Ilg duoc U bao nhrCu?

d) Gili srl do lhdi ddt thay ddi (khi hAu n6ng telr) ngddi ra ghi nhen dddc ti le cdu

ngay cd it nhal01 cu6c goi dci rram li 99./ Theo anh (chi), rram cdn rlng bi ii

nhil bao nhieu xe rhi s€ ddp fng dudc yeu ciu chrla chdy?

CAu 2 : Dd chu6'n bi cho trd chdi "Chung sfc", ngddi ra ra mO! cdD h6i vdi ba ddp itn ( r).

(21 (3) \,:r rh6i1k6 cau trri liti cria 100 neudi nhusau:

D d p a n ( l ) K}I6ng chon dip

i n n i o

a) l'im khodng udc ludng cho ri ie ngLtili chon dtp dn (I) vdi d6 tin c4y 997.

b) Theo quy dinh ngu ti ld ngfdi kh6ng chqn dip 6n nio kh6ng qud 27 rhi kCr qud

Ihdng ke sC dLldc sf dung cho ho chor Vrli mi'c i nghla 57,, arh (chi) hiy cI-,

bi6r kA gui ren sf dung dddc kh6ng'

Ctu 3 i Nghien cflr him luong Vitamir A (7.,) cia mot hai trri cay ta thr duilc k& qud

Him ld.jng

Vitamin A I i-:

1 0 8 1 Gie rhi& ham ludng Vitamir A cia loai ilii crt), niy rrAn lheo luiL chue'n

HIy tim kioang dn cay 927 cho hAm lrrcjrg Vitamin A !rung blnh tr

Neu mu6n ddc ludng lrCn c6 sai sd kh,lng qrI 0,2 7 thi cd cdn

kn6ng? Ndu ci'n thi ph:ii q!an stit rhein i{ nhA't bao nhiSu rral?

Ghi chf : Bing tra can rhiil oho phla sau de rhi

5 - 6 1 2 8 - q

6 - 1 1 1 0 i 9 - 1 0

D'4'g +e

DE IHI MUN : XAC SUAT VA THONG KE TOAIq B

Thdi gia! lem bai : 90 phit

Q!.q! : M6t c6ng nhdn di6u kidn 6 md1' d6!, cdc mdy ney boar dong doc lap vdi nhau vA xdc suei bi

: Sin lddng trung binh cria giSng l{a rruydn rhdng rdng tai ving A le ,18 ralha Ngudi ta dra

SAn liJdns ftalha

N q r v a " r 1 , i N d

cao rruns binh crla mdt boc sinh rrrr<)ng niy

F , t ( l i 1 , 4 8 r n r l r ) c t i c b 5 ' p r ) l ' i n d d ( j c l $ 6 n g ( o = l 7 o ) ' l

v v , \

n ' t " | , r f f , { y 1 r ) : i _ r

- : ! c )

thric xric su{t rltdng ke dC lrnr bai

D i ' r ' I l r x , i c x r j ^ l " r 0 N c t( 0

'l hiti itt0)X 90 tt\it.

xric suiii.'di s:ir 1-.hiirn n:rl li loai A'l

2 / t-ir ngi! rlhien I s;in plri'ru i j k j e D tl u f n h a i t v i 2 s?in p b i n r rir kien lhl2 ' i - | l t r

r ; i i ri r : ;;lrih: lr::i ,^ lirr !i!i,j rli !!r)!! 3 (; D nhtiin lil' r tn 2 ki6n ]

C h o X ( l i n v i { i n h = c n r ) v a r Y ( d d n v r L i D i r = i ( g l lii 2 ciri ti6u ch.iil itrong crln j

l L L , r 1 ' l r i r r r n , l ' t : , , i l s ; , i r r p l r i n ' tr r c ' , t < a r r 1 r i c l r n , " r b l r g s r r r r

)4 t(

l/- llnr pllnjrrg tr)rrh trrung qrrrr tuyCittiDh ntiu ciia

2/.Cirlc rliirr pirii,ii cJ ciri iiCii X irir0lxin 24crrr .,'ir ch!

LI(]c lLitt)g ti 16 srio lrhii"nr loli 2 cri d6 tirr cliy 987o I

3/- l)0 u11c'lLi(rng ti lC srirr lrtrCrn Irli 2 vrli d'j chirrl) xrii- 29 var

cilir cl)i tieU X v(]i d0 chirh xIc 5nrnr vtii cil0g d,i tiri ciiy 9-570

bao rrhiCu sin piriirn riia ?

4/ (;jii sia sru d(i tring I crii li6n ki lhuirl ngliili tr thi)' pi:1 iri trng biDil cLir chjlreu

Y lir 1j,5kg Vr,i nriTc i |ghiii o=0,1) L lliiy chrr nhiu xdt i i cr'ii liin,ki thuit d(i'l

X t h c o Y / Liou \ rlxl L'jn 8kg I:r lo:ri 2.

l n l c l r i ( t n g l n r u ! l b ) n h

t h ) c : i n d i 0 u h 4 t l r 0 u l

,/l

'IltuiJNti

D,]t tt(-rc t).i (L/tlN(]

_ : BtrN t tN ut,x:

t)ii l'rIl xic xu^r'TrrdNC r(ii

T ltiti Ittirtt: 120 llhit

eAU !; Cho I hop t)i t'u)g d(i cai 6 yien (li), 5 vi€n x.nh\, 4 vieu trdng ttLir nlliiu nl)i0o, lin ltftjt, klroDg h,)arn l i cho din khidlrdc viCn di) tl)i dinrg loi.

t liy li!rlr x:;r sui't di:

A / ' , I t l i v i a r r ) : r n l r l i r I v i 0 l l t f i l l l g d ; i ( l o d c r r i t r : r

B/ Kh6ng cr'i vien xlnh nio dri!.,c ftr r:r.

CAI] 2:

Al- Ne,ldinh nrhi^ vir cri0 ti|h

ll/- (lho biit ngdlr nhiin X c6 lr

\li.t rrirr ri',rr:' crl thd dcnr (arn tl drnrc diy tl)a;ns lie sru (/nrr rr)'?S td,)r/.

x c (l).rI) ciir biiJrr nltiitr rrhien Y - )i'

lrhin phiri diu trCrr rip:

c! Mil ngLiiJi din Drul fief lhco, rrrir 2 blo TiDh xdL slrit dt atth {3 InLrir (lLltJc

2 bi() lhur_ic ld1, bioll nsLri,i nrurl lrtl(tc nruA ahidc ba{) thuaic li;t.

N(a, o1),r dai biir Tln $dc iri\ing hop li

tudi) c(i kd{ qu:i sau:

D0 'rur x^c xu('r'r'ndNc t(ii

t t l L l t t L ( ( 1 8 : t z t t l,ltul

a.i 4 J,

'ffong

lUl.ing lr!ng birb cri.r xr)iri Xnin LocbiDg 3(X)g viii s:'i ii6u chuiin

5l37g.q)i lf(jrg lrrinrg c'riu lrtii x()r'ri rtllin rco lh:ir ih(ji chuiiD Xorir airidc aktrrr thiurl) sot Il1di sot l(X) qui Sot dddc goi li lori I ndu tron!i lrrcJns tLikg din 35kg zrl- L4ria I(X):.Ot, lirrlr riiic rj'.!ii't dd cri drillg 5t $JT li)ri 1.

.b/- IVIllI Ii)0s{)t, tinh xIc striit ald c(i tir l20sotloai ltdlcn.

c/- I'lrrii rnu.r rrriiy sLn ilii xric suiit ca, i{ nh,ii t sor lor: t, > t)9,9916.

c l / M 0 t n g r ( J i n r u t l 0 0 s o t k i d n r l i r i c r i 6 4 s o r l o a i 1 , s l l u d i q u a D i u D a v b l t h u 2 sot khorg fa) clr:i1 lrrrrrrg r.di denr vd Bien Il()ar bli N{Ot ng!(ajj din rnua i sor (lfy I-qiill rrhiCn) 'li'rh xric suiit dd ngrtiti itr'r du<tc sot lrrai l-

c'i_ti::

{ ' l x r n , i r r n l : i r r r, l r i r r r ( X r , X , , ) t a i y r n X € N I r 0 ; r 1 ) o : c t l i r l ) j i ( C l \ I l ] j

X , - - ) X , l i r i \ r , i r ' r r t k l r ; i r : c l r : r h r r i , r t ) \ = r :

L ' A U J :

Ei nghien cuLi I iori Lhri iin gi11 srjc |rdi, nguati in tiri r)SiriCnr irCI

clIri,l k lL Ltrr.i tlh snrj ruI't lrnjn! virr n ,,j)

Cho r'i n lltlii irir l 3 9 - .t03 B 0 - I l0(ks)

i L ' n r n l l l i - ' : r I , i, i I e i r i r r o l b/- Dainh bdt 200 c(rr Tirrh xric suii't dd cri 60 con krai I l.

c/- Diinh bd t l0(X] con TiDh i(i1c suii'{ atd ci) lit 29{) con d6i 350 con bai I? d/ Phiri atiuh liritl nhiit rnliyttrn dd-xies a'r itl uhiir I corr loai 1 kh6ng it hdn 99,99'/o l.

af Clro kit luiin vd

bl Udc lltdr)g 1r'org c/-'llnr l.ihorirrg rklc

nghi ugit n6i tron;kidnl na nliic cr=0,05.

lu('ng lrurg binh loai srid lhZirn niy v(ti dO ti| c|y 95o/o [ldng cirxo(x) \,('ii al6 lir cnj, 90-olo

Trong lLrUnts (g)

J r r s : U r p n J t l l

@

Di,;,r'(n x^c xu,{ r rudNc I(t

'I hiti l( tng: l2() l,ttit

| \ ! t t

r.ii ? lr6p rhrriiu l,Y h6p I cl Ta ll grii loai I vi 2 Stii l('iri 2,

grii lolli I !r'r 4 g(ii k)tti 2 I)o srj li, Inc;i liil'l) nrii di I u(ii khQog rd crhlit

tr nl!al] chrirs c,ri 2l'np vi'o lt6p IIl.

l'/ llrr lrir|rr.llrit (la' !tirt X.

!/- X,ic (liDl) 0 rir'lr"^ rl)(ic I'(I X :X|<0) = I

e'i!]

D i i i t | t r ' | | li X ) h i g i i r d l n h n r t a ' i c i L I D N l r ( n r g n i i r l l

( l l r o nhiit) lirh lhc(\ t|iCt| dalng)

a/ 'ljrrll rric sLr(t i;li liihop IIIfN I 86i,dt(Jc I grii lori L

ir/- Ciii li-v r r dcrrr fidnr tfa dt(ic gtii lda i l 't'inh xic srriit ild l:li tiip I g(ii

j ) h i I I 1(ii l1i,y jihan!r'i.

C,:\! L,

{,j 2 bi'rh rl]|]air 1.\'rnaii l)inl) daLr rlrh li) lo ihUix riit,5 lLr xiiLr liiy ngiLr rrhirn

I ltr til irlnh n clro vio blnlt ':] sllrr (li ril hlrth I) lliy rrgiu nhiCll I lo ch vio bl/rh A a,/ I irrh rric rrrft ili ,,ri l,r tlruric Lrolllr tr'trh A rin .kh6ng thiy ddi ii 16 tiit \ii!r -

r l / l i I y n ! l i i , i f q i r i l f r l r h j r l g 1 1 1 i r t l , l r l r \ , r i l u n r i n C ! r L ) r r i j r n i ' i t r i ' i c i ) ,

l i r r i i t ! r 5 ' 1 ,

irl 'llrii | (i hir,)r lirilrg Vitu irirC : ()'r," gri la' urii Iui I i.k]i '1'rr!: ii lii

I li lti/j; ilri,; I ,irrSl i\l Llc i(iiDr I l !j =11,0:i.

al ' L t r r , i , t r L I r \ L \ c l r i u l l l r r r r p r r t : r l ] i n c r : L i r r n ^ l l r r i t f r i i c l l y r l r o 1 r ( x r g l r i L r g

!1li i],l

i r r i r lo i i

!!u !: Cd 216 h)ng : Ld 1 g6ur l0 sin phdm trong d6 c6 2 phd phdm, ld2 gdm 8 sin

phi'm troug d6 c6 1 phd phdm Tr) mdi 16 hing ngddi ta i6,v ng5u nhiOn 2 sAnphdm cdng m6t lric dd udm tra TfiIx?ilu;Gd crro ,

1) Ci 4 sin phdm la'y ra kidm tra diiu li sin phdrn tdt

2), Trong 4 sin phdm lA'y ra kidm tra c6 dilrlg2 ph€ phdJ-UjULU: Didn tich m5r chi€c 1, tbuoc m6t loii ce), ld mor bi6n ngau nhi6n lien tuc X

(ti[h dteo don vr cm2) c6 harn mat d6 :

p ( t ) - i o t ' t - ' ' 1 c ! \ - l u : ' / l

r d i K l a I , i r r r c i

I r t r i , \ + t o l l1) Tlnr K.

- Tioh di6n tich rung bioh cira m6i chidc li cria io)i cay d6.

- Tinh ri lC 16 c6 di6n rich nh6 hdn 1 cm'?

kidm ta ngiu nhi6n 100 iruc ve c6 k6i clui nhu sau :

3) Hdy so sdnh ti 16 phd phdm cria c:{c uuc mi{y ldm ra 1,di ti le phd pha'm choph6p vdi mrlc ! nghia o=0,05 bidt ring cllc mc md1, ph6'phdm ld ciic rruc

4) Hziy ddc lddng ti lQ ph6 phSm cria cric truc rn6y 1dm ra vdi dd rin c{y 954/o

ir,r'rng rheo bar k! rii lieu nio khdc

DE 8,00,

dd kidm ra 'Ilni xdc sud'r dd :

&4.1 : M6t xi nshiep sdD xuai 1 loai ruc mdy vdi chi€u dai qui dinh lA l9,95cm vn ti

ngdu nhi€n 100 rruc cd 16'r qud sau :

y€u ciu rldc ldEng c6 dO rin c6y 95% vi dO chinh xdc 0,08 cm rhr ohai fidrn oumai uuc miiy

3) Hey so srirh d le phd phdm c6c ruc mdv sen xu{r ra vdi ri lC phd pbdm cho phdp

E[dm Ciu I :2d : Clo2 3d I Cau 3 : 5d

Thi sinh kt6ng mang rdi li€u vlo pbdng rhi

J4

lao d6ng c6 qua dAo tao nghd

q = 0,05

vdi dd dn cey 95%

hang ngey uong i sdngiy cria ndm nay , c6 bring rh6ng ke sau :

-12492

i r i 2 5 5 5 5 0 4 91) Nem rudc trung binh m6i ngay biD dudc 225 sAn phdm Cho ring tddng hang bdn

0.05

2) Udc iirorg sd sdn phdm tung binh bdn m hing ngiy ,vdi dO rin cey 957a.(gii thidl

DB 70.t'o ' ,ootQ!y-! : C6 2 hqp bi , hOp 't - chfa 5i./+ 2 bi trong d6 c6 2i bj dd , ( i = 1,2) Ldv ngiunlueo mol ngp r or,

b) La'y ndp I bi Eong hop 1 T:lnh xrc sutt dd duqc bi d6 (ld)

edl? : Cho bidn ngiu nhien len $c X c6 him mdxs :p(x) = Acosx kh; lrl < i I

P ( x ) = u K l u ltl>;;A-nangso.z

a) I tm A b) Tinh EX

!@4-! : Dd ngidin crlu d le si loai A aong 2 16 hing 1 vi tr, ngrrdi ta kidm tra I miu

.a) Udc ldgng d le sfloai A cia Lho I vdi d6 dn cey 95-q (1d)

{u/ha) c6 bAng lhdng ke sau :

Gie tbi€l ndrg sut't lfa X -N (a ;q?)

i j e m L a u I t J o ; L a u / : z o ; u a u J : J o

, 1 , , : ' .

o , l'Ar:)

D E 7 I t z w

mua 2 sf

a) Tim a , b b) Vdi a , b tim duqc , tm tudi thq rung binh loai b6ng dien ften

I nol Cl1eot Sd 16 harg dudc kidm tra sd lo hang bi can fiidu

Th4ng l/2002

Thdns 612402

cnlnn xac tuYo can Xlem lra ir nnar mty lo nanP

56 sf nr

7993