Bi tp Xc Sut Thng K GV L Vn Lai Phin bn 2011 1 Bin ngu nhin Cu 1: Mt kin hng c 5 sn phm tt v 3 sn phm xu. Chn ngu nhin t kin hng ra 2 sn phm (chn 1 ln). a) Lp hm phn phi xc sut ca s sn phm tt chn c; b) Lp hm phn phi xc sut ca s sn phm xu chn c; c) Tnh k vng, phng sai ca s sn phm tt; xu. Cu 2. Kin hng I c 3 sn phm tt v 2 sn phm xu, kin hng II c 2 sn phm tt v 4 sn phm xu. Chn ngu nhin t kin hng I ra 2 sn phm (chn 1 ln) v t kin II ra 1 sn phm. a) Lp hm phn phi xc sut ca s sn phm tt chn c; b) Lp hm phn phi xc sut ca s sn phm xu chn c; c) Tnh k vng, phng sai ca s sn phm tt; xu. Cu 3. Kin hng I c 8 sn phm tt v 2 sn phm xu, kin hng II c 5 sn phm tt v 3 sn phm xu. Chn ngu nhin t kin hng I ra 2 sn phm (chn 1 ln) v b vo kin II, sau t kin II chn ngu nhin ra 2 sn phm. a) Lp bng v hm phn phi xc sut ca s sn phm tt chn c t kin II; b) Lp bng v hm phn phi xc sut ca s sn phm xu chn c t kin II. Cu 4. Mt ngi vo ca hng thy c 5 chic tivi ging nhau. Anh ta ngh c th ln lt tng chic n khi chn c tivi tt th mua v nu c 5 ln th u xu th khng mua. Gi X l s ln th. Bit cc tivi c lp vi nhau v xc sut 1 tivi xu l 0,3. a) Tnh xc sut ngi ny mua c tivi; b) Lp bng phn phi v hm phn phi xc sut ca X. Cu 5. Trong nh ngi A c 7 bng n ging nhau gm 4 bng tt v 3 bng hng. Ngi A em th ln lt (khng hon li) tng bng n cho n khi chn c 2 bng tt th dng. Gi X l s ln th. a) Lp bng phn phi v hm phn phi xc sut ca X. b) Tnh s ln th chc chn nht ngi A c c 2 bng n tt. Cu 6*. C 2 cu th bng r, mi ngi c 3 qu bng. Hai cu th ln lt nm bng vo r cho n khi c ngi nm trng r hoc ht bng th ngng. Bit cu th th nht nm trc, xc sut nm bng trng r ca cu th th nht l 0,7 v ca cu th th hai l 0,8. a) Gi Xi (i = 1, 2) l s ln cu th th i nm. Lp bng phn phi xc sut ca Xi. b) Gi Yi (i = 1, 2) l s ln cu th th i nm trng r. Lp hm phn phi xc sut ca Yi. Cu 7. Cho X l bin ngu nhin c bng phn phi: 1234567 a2a2a3a

Bi tp Xc Sut Thng K GV L Vn Lai Phin bn 2011 2 a) Xc nh tham s a; b) Vi a tm c, tnh P(X > 5) v tm k nh nht sao cho P(X s k) > 0,5 . Cu 8. Mt x th c 6 vin n vi xc sut bn mi vin trng vng 10 ca 1 bia l 0,8. Nu x th bn lin tip 3 vin trng vng 10 th ngng khng bn na. Gi X l s vin n x th bn. a) Tnh P(X > 5) ; b) Lp bng phn phi xc sut ca X; c) Gi Y l s vin n cn li cha bn, lp hm phn phi xc sut ca Y. Cu 9. Theo thng k trung bnh c 1000 ngi dn tui 40 th sau 1 nm c 996 ngi cn sng. Mt cng ty bo him nhn th bn bo him 1 nm cho nhng ngi tui ny vi gi 1,5triung,nungimuabohimchtthstinbithngl300triung.Gis cng ty bn c 10.000 hp ng bo him loi ny (mi hp ng ng vi 1 ngi mua bo him) trong 1 nm. Hi trong 1 nm li nhun trung bnh thu c ca cng ty v loi bo him ny l bao nhiu? Cu 10. Gi X, Y (triu ng) l li nhun thu c khi u t 100 triu ng cho tng d n: a) Tm mc li nhun c nhiu kh nng nht khi u t vo mi d n; b) Xt xem vic u t vo d n no c t ri ro hn; c) Lp bng phn phi xc sut ca Z = 2X + Y. Tnh EZ. Cu 11. Bin ngu nhin lin tc X c hm mt : {

a) Tm a, tnh P(1 < X < 2) v v th hm . b) Tnh EX, VarX. Cu 12. Bin ngu nhin lin tc X c hm phn phi: {

a) Tm hm mt f(x), tnh P(2,5 < X < 3,5) v v th hm F(x). b) Tnh EX, VarX. Cu 13. Bin ngu nhin lin tc X c hm phn phi: {

a) Tm hm mt f(x), tnh P(2,5 < X < 3,5) v v th hm F(x). b) Tnh EX, VarX. Cu 14. Bin ngu nhin lin tc X c hm phn phi: Bi tp Xc Sut Thng K GV L Vn Lai Phin bn 2011 3 {

a) Tm hm mt f(x), tnh(

). b) Tnh EX, VarX. Cu 15. Bin ngu nhin lin tc X c hm mt : {*

+ *

+ a) Tm a, hm phn phiv tnh(

) b) Tnh EX, VarX. Cu 16*. Bin ngu nhin lin tc X c hm phn phi: F(x) = A + B.arctgx, xe . a) Tm A, B, hm mt f(x), tnh P(1s X s1) . b) Tnh EX, VarX, ModX Cu 17*. Bin ngu nhin lin tc X c hm phn phi: {

a) Tm A, B v tnh tnh P(0,5 < X < 0,5) . b) Tm hm mt f(x), EX. Cu 18*. Bin ngu nhin lin tc X c hm mt : {

a) Tm hm phn phi F(x) v tnh tnh P(0,5 < X < 0,5) . b) Tnh EX, VarX, ModX . Cu 19*. Bin ngu nhin lin tc X c hm mt : {

*

+ *

+ a) Tnh EX v tm hm phn phi F(x). b) Tnh xc sut trong 3 php th c lp c 2 ln X nhn gi tr trong khong(

) Phn phi Siu bi v Nh thc Cu 1. T mt nhm 10 k s gm 6 k s ha v 4 k s in chn ngu nhin 4 k s (chn 1 ln). Gi X l s k s in c chn. Bi tp Xc Sut Thng K GV L Vn Lai Phin bn 2011 4 a) Tnh xc sut trong 4 k s c chn c ng 2 k s in. b) Tnh EX v VarX. b) Lp bng phn phi xc sut ca X. Cu 2. Mt l sn phm gm 90 sn phm tt v 10 ph phm. Chn ngu nhin 5 sn phm t l (chn 1 ln). Gi X l s sn phm tt trong 5 sn phm ly ra. a) Tnh xc sut trong 5 sn phm c chn c t nht 2 sn phm tt. b) Tnh EX v VarX. c) Lp bng phn phi xc sut ca X. Cu 3. T b bi 52 l, chn ra (1 ln) 8 l. Gi X l s l c trong 8 l bi chn ra. a) Tnh xc sut trong 8 l bi c chn c t nht 7 l c. b) Tnh EX v VarX. c) Lp bng phn phi xc sut ca X. Cu 4. Mt r mn c 12 tri trong c 5 tri h. Chn ngu nhin t r ra 4 tri. Gi X l s tri mn h chn c. a) Tnh xc sut trong 4 tri c chn c nhiu nht 2 tri khng h. b) Tnh EX v VarX. c) Lp bng phn phi xc sut ca X. Cu 5. Mt l hng c rt nhiu sn phm vi t l ph phm l 0,3%. Kim tra ngu nhin ln lt tng sn phm cal hng ny. Tnh s sn phm ti thiucn kim tra xc sut chn c t nht 1 ph phm khng b hn 91%. Cu6.Mttrngtiuhcctlhcsinhbcnthl0,9%.Kimtrangunhinlnlt tng hc sinh ca trng ny. Tnh shc sinhti thiu cn kim tra xc sut chn c t nht 1 hc sinh b cn th khng b hn 95%. Cu 7. Mt ngi mi ngy mua 1 t v s vi xc sut trng s l 1%. Hi ngi y phi mua lin tip ti thiu bao nhiu ngy c khng t hn 99% hy vng c trng s t nht 1 ln? Cu 8. Gieo 100 ht u, xc sut ny mm ca mi ht l 0,9. Tnh xc sut trong 100 ht: a) C ng 80 ht ny mm; b) C t nht 1 ht ny mm; c) C nhiu nht 98 ht ny mm. Cu 9. Mt k thut vin theo di 14 my hot ng c lp. Xc sut mi my trong 1 gi cn n s iu chnh ca k thut vin ny bng 0,2. Tnh xc sut trong 1 gi: a) C 3 my cn n s iu chnh ca k thut vin. b) S my cn n s iu chnh ca k thut vin khng b hn 3 v khng ln hn 6. Cu10.Mtncngnhnphtrch12mydthotngclp.Xcsutmimydt trong khong thi gian t cn n s chm sc ca n cng nhn bng 0,3. Tnh xc sut trong khong thi gian t: a) C 4 my cn n s chm sc ca n cng nhn. b) S my cn n s chm sc ca n cng nhn khng b hn 3 v khng ln hn 6. Cu11.Bnclp12vinnvo1mctiu,xcsutbntrngcamivinnl0,2. Mc tiu b ph hy hon ton nu c t nht 2 vin n trng vo mc tiu. Tnh xc sut : a) Mc tiu b ph hy 1 phn;b) Mc tiu b ph hy hon ton. Cu12.Bnclp10vinnvo1mctiu,xcsutbntrngcamivinnl0,2. Mc tiu b ph hy hon ton nu c t nht 8 vin n trng vo mc tiu. Tnh xc sut : a) Mc tiu b ph hy hon ton;b) Mc tiu b ph hy 1 phn. Bi tp Xc Sut Thng K GV L Vn Lai Phin bn 2011 5 Cu13*.Mtbithitrcnghimgm12cu,micuc4phngntrlivchc1 phng n ng. Gi s 1 cu tr li ng c 4 im, tr li sai b tr 1 im. Mt sinh vin yu chn cch tr li ngu nhin bng cch chn h ha 1 phng n ca mi cu tr li. a) Tnh xc sut sinh vin t 13 im. b) Tnh xc sut sinh vin b im m. Cu 14. C Ba nui 15 con g mi vi xc sut trng ca mi con trong 1 ngy l 0,6. 1) Tnh xc sut trong 1 ngy c Ba c: a) C 15 con g trng; b) t nht 2 con g trng; c) Nhiu nht 14 con g trng. 2) Nu mun trung bnh mi ngy c 100 trng th c Ba phi nui bao nhiu con g mi ? 3) Nu gi 1 qu trng l 1200 ng th mi ngy c Ba thu c chc chn nht bao nhiu tin? Cu 15*. Trng hai hng cy, mi hng 4 cy. Xc sut mi cy trng sng l 0,8. Trng ln th nht nu cy no cht th trng li cy . Tnh xc sut khng phi trng qu hai ln. Cu 16*. Mt ngi c 3 ch yu thch nh nhau cu c. Xc sut cu c c 3 ch 1, 2, 3 tngng l 0,6; 0,7 v 0,8. Ngi chn ngu nhin 1 ch thcu 3ln v chcu c 1 con c. Tnh xc sut con c cu c ch th 3. Phn phi Poisson Cu 1. Mt trm in thoi t ng nhn c trung bnh 200 cuc gi trong 1 gi. 1) Tm xc sut trm in thoi ny nhn c: a) ng 2 cuc gi trong 1 pht; b) Khng t hn 2 cuc gi trong 1 pht. 2) Tnh s cuc in thoi chc chn nht trm s nhn c trong 16 pht. Cu 2. Trong 1000 trang sch c 100 li in sai. 1) Tm xc sut khi chn ngu nhin 1 trang sch ny c: a) ng 1 li in sai; b) Nhiu hn 3 li in sai. 2) Tnh s li in sai chc chn nht khi chn ngu nhin 45 trang sch ny. Cu 3. Quan st thy trung bnh 5 pht c 15 khch hng vo mt siu th nh. 1) Tm xc sut : a) Trong 1 pht c 4 khch vo siu th; b) C nhiu hn 2 khch vo siu th trong 45 giy. 2) Tnh s khch chc chn nht s vo siu th ny trong 2 gi 18 pht. Cu 4. Quan st thy trung bnh mi ngy c 5 tu cp bn cng A. 1) Tm xc sut : a) Trong 2 ngy lin tip c 8 tu cp bn cng A. b) C t nht 2 tu cp bn cng A trong 6 gi lin tip (mi ngy c 24 gi). 2) Tnh s tu chc chn nht s cp bn cng A trong 2 ngy 15 gi. Cu 5. Mt bn xe khch trung bnh c 40 xe xut bn trong 1 gi. 1) Tnh xc sut : a) Trong 1 pht c 2 xe xut bn; b) Nhiu hn 2 xe xut bn trong 30 giy. 2) Tnh s xe chc chn nht s xut bn trong 1 gi 25 pht. Cu 6. Ti bnh vin A trung bnh 3 gi c 8 ca m. 1) Tm xc sut : a) C 5 ca m trong 2 gi; b) t nht c 2 ca m trong 45 pht. 2) Tnh s ca m chc chn nht s xy ra ti bnh vin trong 1 ngy (24 gi). Cu 7. Quan st thy trung bnh 3 pht c 12 t i cy cu X. 1) Tnh xc sut trong 10 pht lin tip c: a) 40 t i qua cu X; b) T 43 n 46 t i qua cu X. 2) Tnh s t chc chn nht s i qua cu X trong 5 gi 20 pht. Cu 8. Thng k cho thy trung bnh trong 1 tun gi vng thay i 10 ln. 1) Tnh xc sut trong 2 ngy lin tip c: Bi tp Xc Sut Thng K GV L Vn Lai Phin bn 2011 6 a) 5 ln gi vng thay i; b) t nht 2 ln gi vng thay i. 2) Tnh s ln chc chn nht gi vng s thay i trong 1 thng. Cu 9. Trung bnh 1 pht c hai t i qua trm thu ph. a) Tnh xc sut c 6 t i qua trm trong 3 pht; t 3 n 4 t i qua trm trong 2 pht. b) Tnh t xc sut c t nht 1 t i qua trm trong t pht bng 0,99. Cu 10*. Ti 1 nh my trung bnh 1 nm xy ra 1,8 v tai nn lao ng. Tm xc sut : a) Trong vng 5 nm xy ra nhiu nht 3 v tai nn lao ng. b) Trong vng 5 nm lin tip, mi nm xy ra nhiu nht 1 v tai nn lao ng. Cu11*.Mttrmchothuxeconc3chic,hngngyphinpthu100ngnng/chic (cho d xe c c thu hay khng). Gi cho thu l 600 ngn ng/chic. Gi s yu cu khch hng thu xe ca trm l X c phn phi Poisson vi tham s = 2,6 . Gi Y l s tin thu c trong 1 ngyca trm.Lp bng phn phi xcsut caY v t tnh s tin trung bnh thu c ( tr thu) ca trm trong mt ngy. Phn phi chun Cu 1. Cho X N(3; 4) . Tnh

| | | | Cu 2. Cho X c phn phi chun viv . Tnh. Cu 3. Cho X c phn phi chun vi VarX = 25 v . Tnh E(X). Cu 4. Cho X c phn phi chun vi EX = 5 v . Tnh Var(X). Cu 5. Li sut X (%) ca 1 doanh nghip u t vo 1 d n l bin ngu nhin c phn phi chun. Theo nh gi ca y ban u t th li sut cao hn 20% c xc sut l 0,1587; cao hn 25% c xc sut l 0,0228. Vy kh nng doanh nghip u t vo d n trn m khng b thua l l bao nhiu? Cu 6. Thi gian X (thng) t lc vay n lc tr tin ca 1 khch hng ti 1 ngn hng l bin ngu nhin c phn phi chun N(18; 16). Tnh t l (xc sut) khch hng tr tin cho ngn hng: a) Trong khong 12 n 16 thng;b) Khng lu hn 8 thng. c) Ti thiu l bao lu 99% khch hng tr tin cho ngn hng. Cu 7. Thi gian X (tnh bng pht) ca mt khch hng ch c phc v ti 1 ca hng l bin ngu nhin vi X N(4,5; 1,21) . Tnh t l khch phi ch c phc v: a) Trong khong t 3 pht n 5,5 pht; b) Qu 7 pht. c) Thi gian t phi ch l bao nhiu c khng qu 7% s khch phi ch vt qu t. Cu 8*. Chiu cao ca nam gii trng thnh l bin ngu nhin X(cm) c phn phi chun N(163; 25). Hy tm: a) T l (xc sut) nam gii trng thnh cao t 1,60m n 1,70m. b) Chn ngu nhin 1 nam gii trng thnh, tm xc sut ngi ny cao trn 1,65m. c) Xc sut chn ngu nhin ra 5 nam gii trng thnh th c t nht 1 ngi cao trn 1,65m. Cu9*.ChiudimtloitrcmyonhmyAsnxutralbinngunhinX(cm)c phn phi chun. Bit chiu di trung bnh ca loi trc my l v lch chun l .GilchnhxccaXnu||.Hichnhxccachiudisn phm l bao nhiu c t l 80% trc my t chnh xc ny. Bi tp Xc Sut Thng K GV L Vn Lai Phin bn 2011 7 Cu 10*. Mt chi tit my c tin vi bn knh quy nh l R = 1cm. Gi s bn knh ca cc chi tit my sn phm l bin ngu nhin X(cm) c phn phi chun. Tm lch tiu chun ca cc bn knh chi tit my sn phm sao cho vi t l 90% bn knh chi tit my sn sut ra lch khi mc quy nh khng qu 0,01cm (thng c gi l dung sai). Cu 11*. Mt doanh nghip cn mua 1 loi trc my c ng knh t 1,18cm n 1,22cm. C hai nh my bn loi trc my ny v ng knh cc loi trc my c sn xut ra l bin ngu nhin X, Y c phn phi chun vi cc s c trng: ng knh trung bnh (cm) lch tiu chun (cm)Gi bn (ng) Vy doanh nghip nn mua trc ca nh my no? Mt s xp x xc sut thng dng Cu 1. Mt bao thc c t l ht lp l 0,01%. Chn ngu nhin lin tip 5000 ht. Tnh xc sut : a) C ng 2 ht thc lp; b) C t nht 2 ht thc lp. Cu 2. Mt hng sn xut trung bnh 1000 a nhc th c 1 a hng. Tnh xc sut khi hng sn xut 9000 a nhc th c nhiu hn 10 a khng hng. Cu 3. Xc sut sinh b gi l 51%. Tnh xc sut trong 500 b sp sinh ti 1 bnh vin c: a) S b gi khong t 150 n 170; b) t nht c 180 b gi. Cu4.Mtvnlanc60000cyspnhoa,trongc7000cyhoamu.Chnngu nhin 200 cy lan trong vn ny. Tnh xc sut chn c 75 cy lan c hoa mu . Cu 5. Mt l hng c 1% ph phm. Tnh xc sut khi chn 1000 sn phm t l hng c: a) Tt c u tt; b) C t nht 2 ph phm. Cu 6. Trong mt phng c 40% ngi nghin thuc l. Chn ngu nhin 300 ngi (chn c lp). Tnh xc sut trong c khng qu 140 ngi nghin thuc l. Cu 7. Mt cng ty nhp 5000 thng ha cht, trong c 1000 thng km cht lng. Cng ty ny phn phi ngu nhin 10 thng (khng hon li) cho 1 ca hng. Tnh xc sut ca hng ny nhn 3 thng km cht lng. Cu 8*. Mt my sn xut t ng vi t l sn phm hng l 0,02. Vi t l khng nh hn 0,97 c th ni: Trong 1000 sn phm do my lm ra th s ph phm nm trong khong no? Cu 9*. Mt k tc x (KTX) c 1000 sinh vin, nh n phc v ba tra lm 2 t lin tip. S ch ngi ca nh n ti thiu l bao nhiu t l sinh vin khng c ch ngi t hn 0,01? Vector ngu nhin ri rc Cu 1. Gii tnh X (N: 0; Nam: 1) v thu nhp Y (triu ng / thng) ca cng nhn cng ty A c bng phn phi ng thi cho bi:

1) Lp bng phn phi xc sut v thu nhp ca cng nhn cng ty A. 2) Lp bng phn phi xc sut v gii tnh ca cng nhn cng ty A. 3) Lp bng phn phi xc sut thu nhp ca n cng nhn cng ty A. 4) Lp bng phn phi xc sut thu nhp ca nam cng nhn cng ty A. 5) Tm xc sut thu nhp ca cng nhn n c thu nhp trn 2,5 triu ng / thng. Bi tp Xc Sut Thng K GV L Vn Lai Phin bn 2011 8 6) Tm xc sut thu nhp ca mt cng nhn c thu nhp trn 2,5 triu ng / thng, bit ngi ny l nam. 7) Tm thu nhp trung bnh ca cng nhn cng ty A. 8) Tm thu nhp trung bnh ca nam cng nhn cng ty A. Cu 2. Ngi ta thng k v trnh hc vn X (Tiu hc: 0; Trung hc: 1; i hc: 2) v tui Y i vi nhng ngi trong tui lao ng ca tnh A c bng phn phi ng thi cho bi:

1) Lp bng phn phi xc sut v trnh hc vn ca ngi dn (trong tui lao ng) tnh A. 2) Lp bng phn phi xc sut v tui ca ngi dn (trong tui lao ng) tnh A. 3) Lp bng phn phi xc sut v tui ca nhng ngi c trnh i hc. 4) Lp bng phn phi xc sut v trnh hc vn ca nhng ngi c tui 39. 5) Tm xc sut ca mt ngi c trnh trung hc tr ln, bit ngi ny c tui 24. Cu3.ChiphqungcoX(triung)vdoanhthuY(triung)cacngtyAcbng phn phi ng thi cho bi: 1) Tnh doanh thu trung bnh ca cng ty A. 2) Tnh chi ph qung co trung bnh ca cng ty A. 3) Bit doanh thu ca cng ty A l 500 triu ng, hy lp bng phn phi v chi ph qung co. 4)Lp bng phn phi xc sut v doanh thu ca cng tyA, bit chi phqung co l 80 triu ng. 5) Bit doanh thu ca cng ty A l 700 triu ng, hy tnh chi ph qung co trung bnh. 6) Bit chi ph qung co l 50 triu ng, hy tnh doanh thu trung bnh.Cu 4. Li sut ca c phiu X (%) v c phiu Y (%) c bng phn phi ng thi cho bi: 1) Tnh li sut trung bnh ca c phiu X, li sut trung bnh ca c phiu Y. 2) Lp bng phn phi xc sut li sut ca c phiu Y khi li sut ca c phiu X l 12%. 3) Tnh li sut trung bnh ca c phiu X khi li sut ca c phiu Y l 5%. 4) Tnh li sut trung bnh ca c phiu Y khi li sut ca c phiu X l 3%. 5) Tnh li sut ca c phiu X khi li sut ca c phiu Y khng m. Bi tp Xc Sut Thng K GV L Vn Lai Phin bn 2011 9 Vector ngu nhin lin tc Cu5.TuithX(nm)vthigiansdngmingyY(gi)camtchititmychm mt : {

1) Tm hm mt ca X, ca Y. 2) Tm tui th trung bnh ca chi tit my v trung bnh thi gian s dng ca chi tit my trong 1 ngy. 3) Tm hm mt ca X khi bit thi gian s dng ca chi tit my trong 1 ngy l 1 gi. 4) Tm hm mt ca Y khi bit tui th ca chi tit my l 1 nm. 5) Bit mi ngy s dng chi tit my 1 gi, hy tm tui th trung bnh ca chi tit my ny. Cu 6. Nng sut la X (tn/ha) v lng phn bn Y (100kg/ha) c hm mt : {

1) Tm hm mt ca X, ca Y. 2) Tnh EX, EY. 3) Tm cc hm mt

|

| 4) Bit nng sut la l 5 tn/ha, hy tm lng phn bn trung bnh. 5) Tm nng sut la trung bnh khi lng phn bn l 150 kg/ha. BI TP THNG K I. C LNG KHONG Cu 1. Ngi ta kim tra ngu nhin 400 sn phm ca 1 nh my th thy c 20 ph phm. Vi tin cy 95%, hy c lng t l chnh phm ca nh my ny? Cu 2. iu tra ngu nhin 100 thanh nin 1 vng qu thy c 45 ngi tt nghip THPT. Vi tin cy 97%, hy c lng t l thanh nin tt nghip THPT vng qu ny? Cu 3. Trong kho c 10000 hp tht, kim tra ngu nhin 100 hp thy c 5 hp b hng. Vi tin cy 93%, hy c lng trong kho ny c khong bao nhiu hp b hng. Cu 4. Trong kho c 1000 sn phm ca nh my A sn xut b ln vi nhiu sn phm do nh my B sn xut. Ly ngu nhin t kho ra 100 sn phm thy c 9 sn phm do nh my A sn xut. Vi tin cy 92%, hyc lng trongkho nyc khong baonhiu sn phm do nh my B sn xut. Cu 5. c lng s di c trong 1 hang ng ngi ta bt 3200 con, nh du ri th li vo hang.Mtthigiansau,ngitabtli400contronghangnyththy65concnhdu. Vi tin cy 97%, hy c lng s di c trong hang ng . Cu 6. Chn ngu nhin 36 cng nhn ca 1 nh my th thy mc lng trung bnh l 960 ngn ng/thng. Gi s mclng ca cng nhn tun theo quy lut chun vingn ng. Vi tin cy 95%, hy c lng mc lng trung bnh ca cng nhn trong ton nh my. Cu 7. Sn lng trong ngy ca 1 phn xng l bin ngu nhin c phn phi chun, kt qu thng k trong 10 ngy l: 26; 23; 27; 26; 21; 28; 25; 30; 26; 23. Hy c lng sn lng trung bnh trong 1 ngy ca phn xng vi tin cy 90%. Cu 8. Theo di 100 sinh vin ca trng A xc nh s gi t hc nh th thy c 95 sinh vin c t hc vi s gi trung bnh 4,01 gi vi s = 1,54 gi. Bi tp Xc Sut Thng K GV L Vn Lai Phin bn 2011 10 a) c lng s gi t hc ca sinh vin trng A vi tin cy 97%. b) c lng t l sinh vin trng A khng t hc vi tin cy 90%. Cu 9. o ng knh d (mm) ca 100 chi tit my do 1 x nghip sn xut c s liu: 19,80 19,85 19,85 19,90 19,90 19,95 19,95 20,00 20,00 20,05 20,05 20,10 20,10 20,15 20,15 20,20 351628231474 Quy nh nhng chi tit my c ng knh t 19,9mm n 20,1mm l t chun. a) c lng t l chi tit my t chun vi tin cy 99%. b) c lng ng knh trung bnh ca chi tit my t chun vi tin cy 95%. Cu 10. Nng sut la trong 1 vng l bin ngu nhin. iu tra ngu nhin 100ha ca vng ny, ngi ta thu c bng s liu: Nng sut (t/ha)41444546485254 Din tch (ha)1020301510105 a) c lng nng sut la trung bnh ca vng trn vi tin cy 95%. b) Nhng tha rung trong vng trn c nng sut t 48 t/ha tr ln l nhng tha c nng sut cao. c lng t l din tch c nng sut cao vi tin cy 97%. Cu11.Nngsutlatrong1vnglbinngunhin.Gtngunhin115hacavngny, ngi ta thu c bng s liu: Nng sut (t/ha)40 - 4242 - 4444 - 4646 - 4848 - 5050 - 52 Din tch (ha)102030151010 a) c lng nng sut la trung bnh ca vng trn vi tin cy 95%. b)Nhngtharungtrongvngtrncnngsutkhngqu44t/halnhngthacnng sut thp (gi s c phn phi chun). c lng nng sut la trung bnh ca nhng tha rung c nng sut thp vi tin cy 99%. Cu 12. Ngi ta xp 100 tri i vo 1 thng, c rt nhiu thng nh th. Kim tra ngu nhin 50 thng thy c 100 tri i khng t tiu chun. a) c lng t l tri i khng t tiu chun vi tin cy 97%. b) Mun c lng t l tri i khng t tiu chun vi chnh xc nh hn 0,1% v tin cy 99% th cn phi kim tra ti thiu bao nhiu thng? c) Nu c lng t l tri i khng t tiu chun vi chnh xc 0,5% th m bo tin cy l bao nhiu? Cu 13. Ngi ta xp 100 tri i vo 1 thng, c rt nhiu thng nh th. Kim tra ngu nhin 50 thng thy c 450 tri i khng t tiu chun. a) c lng t l tri i khng t tiu chun vi tin cy 95%. b) Nu c lng t l tri i khng t tiu chun vi chnh xc 0,5% th m bo tin cy l bao nhiu? c)Nuclngtltriikhngttiuchunvitincy99,7%thchnhxct c bao nhiu? Cu 14. Kt qu quan st v hm lng Vitamin c trong 1 loi tri cy, thu c bng s liu: Hm lng (%)6 77 88 99 1010 1111 - 12 S tri5102035255 a) c lng hm lng Vitamin c trong 1 tri cy trn vi tin cy 95%. b) Nhng tri cy c hm lng Vitamin trn 10% l tri cy loi I. Hy c lng t l tri cy loi I vi tin cy 99%. Bi tp Xc Sut Thng K GV L Vn Lai Phin bn 2011 11 c) Mun c chnh xc khi c lng hm lng Vitamin c trong 1 tri cy trn nh hn 0,1 vi tin cy 95% th cn quan st thm ti thiu bao nhiu tri cy na? Cu 15. Thng k im trung bnh mn ton ca 100 th sinh thi vo trng i hc A l 5,25 vi s = 2,5. a) c lng im trung bnh mn ton ca th sinh vi tin cy 97%. b)Bitchnhxccaclngcua)l0,25im,hyxcnhtincycac lng? Cu 16. Tui th ca 1 loi bng n A l bin ngu nhin c phn phi chun, vi = 100 gi. Chn ngu nhin 100 bng n A th nghim th thy tui th trung bnh ca mi bng l 1000 gi. a) c lng tui th trung bnh ca bng n A vi tin cy l 95%. b) Vi chnh xc ca c lng tui th trung bnh bng A l 15 gi, hy xc nh tin cy? c) Nu mun c chnh xc ca c lng tui th trung bnh bng n A ln hn 25 gi v tin cy l 97% th cn th nghim ti a l bao nhiu bng n A? Cu 17. Trng lng cc bao bt m ti ca hng A l bin ngu nhin c phn phi chun. Cn ngu nhin 20 bao th thy trng lng trung bnh ca mi bao l 48kg v s = 0,5kg. a) c lng trng lng trung bnh ca 1 bao bt m ca hng A vi tin cy l 95%. b) Vi chnh xc ca c lng trng lng 1 bao bt m l 0,26kg, hy xc nh tin cy? c) Vi chnh xc ca c lng trng lng 1 bao bt m ln hn 0,16kg v tin cy l 97% th cn cn ti a bao nhiu bao bt m? Cu 18. Ngi ta kim tra ngu nhin 100 hp tht trong 1 kho th thy c 11 hp khng t tiu chun. a) c lng t l hp tht t tiu chun trong kho vi tin cy 94%. b) Vi chnh xc (sai s) cho php khi c lng t l hp tht khng t tiu chun trong kho l 3% th m bo tin cy l bao nhiu? c) Vi sai s cho php khi c lng t l hp tht khng t tiu chun trong kho l 1% v tin cy l 99% th cn kim tra ti thiu bao nhiu hp tht? Cu 19. Mt l hng c 5000 sn phm. Kim tra ngu nhin 400 sn phm t l hng thy c 360 sn phm loi A. a) c lng s sn phm loi A c trong l hng ny vi tin cy 96%. b) Nu mun c lng s sn phm loi A ca l hng vi sai s ( chnh xc) nh hn 150 sn phm v tin cy 99% th cn kim tra ti thiu bao nhiu sn phm? Cu 20. Tui th (tnh bng thng) ca 1 loi thit b A l bin ngu nhin c phn phi chun. Ngi ta th nghim ngu nhin 15 thit b A, c kt qu: 114; 78; 96; 137; 78; 103; 126; 86; 99; 114; 72; 104; 73; 86; 117. a) c lng khong cho trung bnh v phng sai ca tui th thit b A vi tin cy 95%. b) Nu mun c tin cy 99% v chnh xc nh hn 4 thng ca c lng tui th ca thit b A th cn th nghim thm bao nhiu thit b na? Cu 21. Gim c ngn hng A mun c lng s tin gi ca mt khch hng bng cch chn ngu nhin 30 khch th thy: S tin gi trung bnh l 4750$ v lch tiu chun l 200$. a) Vi tin cy 95%, c lng s tin gi ca mt khch hng ti ngn hng A? b)Numuncchnhxccaclngtrungbnhl300$thmbotincylbao nhiu? c) Nu mun c chnh xc ca c lng trung bnh nh hn 300$ v tin cy 99% th cn chn ti thiu bao nhiu khch hng? Bi tp Xc Sut Thng K GV L Vn Lai Phin bn 2011 12 Cu 22. c lng doanh thu ca 1 cng ty gm 380 ca hng trn ton quc trong 1 thng, ngi ta chn ngu nhin 10% s ca hng v c bng doanh thu trong 1 thng: Doanh thu (triu ng/thng)20406080 S ca hng816122 a)Vitincy97%,clngdoanhthucamicahngvtngdoanhthucacngty trong 1 thng. b)Numuncchnhxccaclngdoanhthucamicahngtrong1thngl0,5 triu ng th m bo tin cy l bao nhiu? Cu23*.Tlnxuti1ngnhngltsgiatngsnquhnvtngsnchovay ang c thc hin. T l n xu ca cc ngn hng vng A l bin ngu nhin c phn phi chun. iu tra ngu nhin 7 ngn hng vng A th thy t l n xu l: 7%; 4%; 6%; 7%; 5%; 4%; 9%. Nhn vin thanh tra phn nn rng t l n xu cc ngn hng vng A cao hn vng B v ch c 3,7%. Vi tin cy 95%, hy dung c lng khong t l n xu trung bnh ca vng A xem li phn nn trn c ng khng? Cu hi tng t vi tin cy 99%? Cu24.nghincunhucuvloihngA1khuvcngitatinhnhkhost400 trong ton b 10000 gia nh, kt qu: Nhu cu (kg/thng)0 22 44 66 88 1010 1212 1414 16S gia nh10358613278311810 a) c lng nhu cu v loi hng A ca khu vc trn trong 1 nm vi tin cy 95%. b) Mun c c lng trn vi chnh xc nh hn 5 tn v tin cy 95% th cn kho st ti thiu bao nhiu gia nh trong khu vc? Cu 25. Cng ty A tin hnh kho st nhu cu tiu dng v 1 loi sn phm do cng ty sn xut trong 1 thnh ph c 600000 h dn. Kt qu kho st 500 h dn th c 400 h dng loi sn phm ny: Nhu cu (kg/thng)0,5 1,01,0 1,51,5 2,02,0 2,52,5 3,03,0 3,5 S gia nh4070110906030 a) Nu mun c lng t l h dn c nhu cu v loi sn phm ny vi tin cy 97% v chnh xc nh hn 3% th cn kho st ti thiu bao nhiu h dn? b) c lng s lng loi sn phm ny ca cng ty A c tiu th thnh ph trong 1 nm. Cu 26. nh gi mc tiu th in ca 10000 h dn trong vng A, cng ty in lc tin hnh kim tra ngu nhin 400 h th c kt qu: Mc tiu th (100KW/thng)0 1 1 2 2 3 3 4 4 5 5 6S gia nh20110150644610 a) c lng mc tiu th in ca mi h dn vng A trong 6 thng vi tin cy 97%. b) Nhng h dn c mc tiu th in trn 400kw/thng l nhng h tiu th in cao. c lng s h dn c mc tiu th in cao trong vng A vi tin cy 95%. Cu27.Mchaophnguynliucho1nvsnphmXlbinngunhincphnphi chun. Quan st 28 sn phm ny ngi ta thu c bng s liu: Nguyn liu hao ph19,0 19,520,020,5 S sn phm56143 a) c lng mc hao ph cho 1 n v sn phm X vi tin cy 97%. b) Nh my A ang sn xut mi ngy 10000 sn phm X. Bit rng gi nguyn liu sn xut snphmAbntrnthtrngl2000ng/gr,hyclngxemmingynhmyAb thit hi khong bao nhiu tin hao ph cho loi sn phm X? Bi tp Xc Sut Thng K GV L Vn Lai Phin bn 2011 13 Cu28.ScchulcX(kg/cm2)caximngdonhmyAsnxutlbinngunhinc phn phi chun. Ngita chn ngu nhin 28 mu ximng ny kim tra sc chu lc, kt qu: 10,0; 13,0; 13,7; 11,5; 11,0; 13,5; 12,2; 13,0; 10,0; 11,0; 13,5; 11,5; 13,0; 12,2; 13,5; 10,0; 10,0; 11,5; 13,0; 13,7; 14,0; 13,0; 13,7; 13,0; 11,5; 10,0; 11,0; 13,0. Vi tin cy 95%, hy c lng: a) Sc chu lc ca ximng do nh my A sn xut. b) T l ximng c sc chu lc km (di 13 kg/cm2) do nh my A sn xut.Cu 29. Mt nng dn gieo th nghim 1000 ht ca 1 ging la mi th c 640 ht ny mm. a) Vi tin cy 95%, hy c lng t l ny mm ca ging la ny? b) Nu mun m bo tin cy 97% v chnh xc ca c lng t l ht la ny mm nh hn 1% th ngi nng dn cn gieo ti thiu bao nhiu ht? Cu 30. nh gi tr lng c c trong 1 h ngi ta nh bt 2000 con, nh du ri th li xung h. Sau 1 thi gian bt li 400 con th thy 80 con c nh du. a) c lng tr lng c c trong h ny vi tin cy 95%. b) Nu mun chnh xc ca c lnggimhn mt na th ln sauphi bt ti thiu my con c? Cu31.Ngitatinhnhiutrathtrngv1loisnphmmibngcchphngvn ngu nhin 300 khch hng th thy c 90 ngi thch sn phm ny. a) c lng t l khch hng thch sn phm ny vi tin cy 95%. b) Nu mun m bo tin cy 95% v chnh xc ca c lng t l trn nh hn 1% th cn phng vn thm ti thiu bao nhiu ngi na? c) Vi mu iu tra trn v chnh xc ca c lng t l l 0,0436 th m bo c tin cy l bao nhiu? Cu 32. iu tra ch tiu X (c phn phi chun v tnh bng %) ca 1 s sn phm cng loi ta c: X0 55 1010 1515 2020 2525 3030 3535 40 n7122025181251 Quy c nhng sn phm c ch tiu X khng qu 10% l loi 2. a) c lng t l sn phm loi 2 vi tin cy 99%. b) Nu dng s liu ca mu c lng trung bnh ch tiu X vi tin cy 95% v chnh xc nh hn 1% th cn iu tra ti thiu thm bao nhiu sn phm na? Cu 33. Mt cng ty in t tin hnh iu tra th trng v s thch xem tivi ca c dn trong 1 thnh ph. iu tra ngu nhin 40 ngi th thy s gi xem tivi trung bnh ca mi ngi trong 1tunll15,3givilchtiuchunmuhiuchnhl3,8givc27ngixemtin m t nht 3 ln trong 1 tun. a) c lng t l c dn trong thnh ph xem tin m t nht 3 ln 1 tun vi tin cy 95%. b)Kchthcmuiutratithiulbaonhiunuvitincy95%,cngtymunc lng thi gian xem tivi ca mi c dn c chnh xc nh hn 20 pht? c)Kchthcmuiutratithiulbaonhiunuvitincy99%,cngtymunc lng t l ngi xem tin m t nht 3 ln 1 tun c chnh xc nh hn 2,5%? Cu 34. Li sut c phiu ca cng ty A l bin ngu nhin c phn phi chun. Trong 10 nm qua li sut c phiu ca cng ty A (tnh bng %) ln lt l 15; 10; 20; 7; 14; 9; 8; 13; 12; 12. a) c lng li sut c phiu ca cng ty A trong 1 nm vi tin cy 99%. b)Gismtngimua1000cphiucacngtyA,mnhgi50000ng/cphiu,trong nm nay. Hy c lng tin li ngi ny thu c vo cui nm t c phiu ca cng ty A? Bi tp Xc Sut Thng K GV L Vn Lai Phin bn 2011 14 Cu 35. iu tra ngu nhin 300 khch hng v mc yu thch 1 loi sn phm A th thy c 90 ngi yu thch.a)Vitincy98%,hychobittlthpnhtvcaonhtcakhchhngyuthchsn phm A? b)NumunclngtlyuthchsnphmAcakhchhngvitincy98%v chnh xc nh hn 1,5% th cn phi iu tra thm ti thiu bao nhiu khch hng na? Cu36.Dngphngphphpthnguyntphntchlngkmctrongtc,mtk thut vin phn tch 35 mu tc, kt qu (X l lng km trong tc, n v: ppm (phn triu)): X188190193195196198199204 n345107321 a) c lng lng km c trong tc vi tin cy 95%. b)Numunclnglngkmctrongtcvitincy97%vchnhxcnhhn 3ppm th cn phn tch ti thiu bao nhiu mu tc? II. KIM NH GI THUYT Cu 1. T l ph phm do cng ty A sn xut l 5%. Nhm gim t l ph phm, cng ty A ci tin k thut. Sau ci tin, ngi ta kim tra ngu nhin 400 sn phm thy c 18 ph phm. Vi mc ngha 5%, hy cho kt lun v hiu qu ca vic ci tin k thut ca cng ty A? Cu 2. im danh ngu nhin 100 sinh vin khoa Kinh t thy c 8 ngi vng, im danh 120 sinh vin khoa C kh thy c 12 ngi vng. Vi mc ngha 2%, hy cho bit mc chuyn cn ca sinh vin hai khoa trn? Cu 3. T l bnh nhn c cha khi bnh bng loi thuc c l 80%. Ngi ta a vo mt loi thuc mi iu tr cho 1100 bnh nhn th thy c 920 ngi khi bnh. Nu ni rng loi thuc mi iu tr c hiu qu hn th c chp nhn c khng vi mc ngha 4%? Cu4.Mtcngtyinthoinirngslptinthoichokhchhngtrongthnhph chmnhtl30ngyktkhicyucu.Kimtrangunhin30khchhngthythigian trungbnhchlpinthoil34,5ngyvilchmuhiuchnhl3,3ngy.Vimc ngha 3%, c th chp nhn li tuyn b ca cng ty c khng? Cu5.TrnglngmtloisnphmdonhmyAsnxutcphnphichunvtrng lng quy nh l 500gr. Nghi ng trng lng c xu hng gim st, ngi ta cn ngu nhin 25 sn phm loi ny v c bng s liu: Trng lng (gr)480485490495500510 S sn phm238534 Vi mc ngha 0,05, hy cho kt lun v iu nghi ng ni trn? Cu 6. im mn XSTK ca 1 s sinh vin hai khoa nh sau: Khoa XKhoa Y im567891045678910 S SV2412156212591861 Vi mc ngha 0,03, c nhn xt g v im trung bnh mn XSTK ca sinh vin hai khoa? Cu 7. Mt dy chuyn sn xut bng n c gi l hot ng bnh thng nu tui th trung bnh ca bng n sn xut ra l 375 gi. Kim tra ngu nhin 70 bng n loi ny th thy tui th trung bnh l 350 gi v s = 60 gi. Vi mc ngha 5%, hy cho bit dy chuyn sn xut bng n ny c hot ng bnh thng khng? Bi tp Xc Sut Thng K GV L Vn Lai Phin bn 2011 15 Cu8.Ngitakimtrangunhin100chaincngtloi2ltdonhmyAsnxutth thy lng nc ngt trung bnh trong chai l 1,99 lt v s = 0,05 lt. Vi mc ngha 1%, hy cho bit lng nc ngt trong chai loi ny c b thiu khng? Cu 9. Mt t kim tra mun xc nh thi gian trung bnh t lc cng ty A nhn n khiu ni ca khch hng n lcgii quyt l bao nhiu ngy, h chn ngu nhin 15 trng hp khiu ni trong nm qua th c kt qu (n v: ngy): 114; 78; 96; 137; 78; 103; 117; 126; 86; 99; 114; 72; 104; 73; 96. Gi s s ngygii quyt khiu ni ca cng tyA l bin ngu nhin cphn phi chun. Vi mc ngha 1%, c th cho rng thi gian 1 khiu ni c gii quyt bi cng ty A vt qu 90 ngy khng? Cu 10. Mt cng ty tuyn b rng 75% khch hng a thch sn phm ca mnh. iu tra ngu nhin400khchhngththyc260ngiathchsnphmcacngty.Vimcngha 3%, hy cho kin v li tuyn b trn? Cu 11. Mt l hng c xem l tiu chun xut khu nu t l ph phm khng vt qu 0,3%. Kim tra ngu nhin 1200 sn phm ca l hng ny th thy c 4 ph phm. Vi mc ngha 5%, hy cho bit l hng trn c c php xut khu khng? Cu 12. Trong nm trc, s tin gi tit kim bng ngoi t trung bnh ca mi khch hng l 1000 USD/nm. nh gi xem xu hng ny c c gi nguyn trong nm nay hay khng, ngitakimtrangunhin64stitkimththystingitrungbnhcamisl 990USD/nm v lch tiu chun hiu chnh l 100USD/nm. Vi mc ngha 3%, hycho bit s tin gi tit kim ca khch hng c thay i khng? Cu 13. Trc bu c ngi ta thm d 10000 c tri th thy c 3900 ngi ni rng s b phiu chongA.Mttunsau(vnchabuc),ngitatchc1cucthmdkhcvthyc 6890 trong s 15000 c tri c hi s b phiu cho ng A. Vi mc ngha 5%, t l c tri s b phiu cho ng A c thay i khng? Cu14.Haimycnggiacngmtloichitit.kimtrachnhxccahaimyny ngi ta o ngu nhin 7 chi tit do mi my gia cng (n v: mm): My 1135138136140138135139 My 2140135140138135138140 Vi mc ngha 1%, c th xem 2 my c chnh xc nh nhau khng? Bit rng kch thc chi tit do cc my gia cng c phn phi chun. Cu15.kimtrathigiansnxutra1snphmcngloicahaimy(nv:giy), ngi ta theo di ngu nhin c hai my v ghi li kt qu: My 158585638703842756867 My 257556324674333685654 Vimcngha5%,cthxem2mycthigiansnxutraloisnphmtrnnhnhau khng? Bit rng thi gian sn xut ra 1 sn phm trn do cc my sn xut c phn phi chun. TNG HP Cu 1. Thu nhp (triu ng / nm) ca 80 h dn trong bn A l bin ngu nhin c phn phi chun. Trong nm nay, ngi ta iu tra ngu nhin v thu nhp ca 40 h dn trong bn A, c bng s liu: Bi tp Xc Sut Thng K GV L Vn Lai Phin bn 2011 16 Thu nhp4,04,55,05,56,06,57,07,58,0 S h134687632 a) Vi tin cy 95%, hy c lng mc thu nhp ca 1 h dn bn A. b) Vi tin cy 95%, hy c lng s h dn ca bn A c thu nhp di 5 triu ng / nm. c) Nu bit trc y 2 nm thu nhp bnh qun ca cc h dn trong bn A l 5,5 triu ng / nm, vi mc ngha 3% c nhn xt g v mc sng ca dn trong bn A hin nay? Cu2.Mcthunhp(triung/thng)canhnvintrong1cngtyncngoiAlbin ngu nhin. Kho st ngu nhin mt s nhn vin cng ty A, c kt qu: Thu nhp8 10 10 12 12 14 14 1616 18 18 20 20 22 22 24S h12356647242063 a) c lng mc thu nhp ca 1 nhn vin cng ty A vi tin cy 97%. b)Numunclngmcthunhpca1nhnvincngtyAvitincy99%v chnh xc nh hn 0,3 triu ng / thng th cn kho st ti thiu bao nhiu nhn vin? c)Nhngnhnvincmcthunhptrn18triung/thnglcthunhpcao(gisc phn phi chun). Vi tin cy 98%, hy c lng mc thu nhp ca 1 nhn vin c thu nhp cao? d) C ngi ni t l nhn vin c thu nhp cao cng ty A l 13%, vi mc ngha 1% c nhn xt g v li ni trn? Cu 3. Trong kho c rt nhiu sn phm ca x nghip A, trng lng X (kg) ca cc sn phm ny l bin nhin. Cn ngu nhin 1 s sn phm loi ny, c kt qu: X (kg)0,80,850,85 0,90,9 0,950,9511 1,051,05 1,11,1 1,15 S sn phm5102030151010 a) C ngi ni rng nh p dng k thut mi lm trng lng sn phm ny t n hn 1kg. Vi mc ngha 5%, c nhn xt g v li ni trn? b) Cc sn phm c trng lng X > 1,05kg l loi 1 (gi s c phn phi chun). Vi tin cy 98%, hy c lng trng lng ca cc sn phm loi 1. c) Nu mun m bo tin cy ca c lng t l cc sn phm loi 1 l 80% v chnh xc nh hn 3% th cn phi cn ti thiu bao nhiu sn phm? d) Gi s trong kho c ln 1000 sn phm ca x nghip B. Ly ngu nhin t kho ra 100 sn phm th thy c 9 sn phm ca x nghip B. Hy c lng s lng sn phm ca x nghip A c trong kho vi tin cy 90%? Cu 4. Ch tiu cht lng X (gram) ca 1 loi sn phm l bin ngu nhin. Kim tra ngu nhin 1 s sn phm loi ny, c kt qu: 240; 200; 260; 220; 200; 280; 260; 260; 240; 260; 280; 240; 260; 220; 240; 240; 240; 260; 240; 220; 280; 260; 280; 260; 280; 280; 240; 260; 240; 220; 280; 260; 260; 220; 260; 260; 260; 260; 240; 240; 220; 260; 240; 220; 240; 240; 240; 200; 240; 260. a) Cc sn phm c ch tiu X < 240gr l sn phm loi 2 (gi s c phn phi chun). C ti liu ni rng trung bnh ch tiu X ca cc sn phm loi 2 l 220gr, vi mc ngha 2% c nhn xt g v ti liu ny? b)ChobitchtiuYcasnphmnythaY=0,4X+0,35.Vitincy97%,hyc lng trung bnh ca ch tiu Y? Bi tp Xc Sut Thng K GV L Vn Lai Phin bn 2011 17 Cu5*.KimtrangunhinmtssnphmcaxnghipAvchiudiX(cm)vhm lng cht Y (n v tnh l %), c kt qu: Y 810121416 X 10055 110467 120598 130469 14057 a) Gi 1m sn phm ny l 30 ngn ng. Vi tin cy 98%, hy c lng gi trung bnh ca sn phm x nghip A? b)CcsnphmcX 110cm vY 12% lloi2(giscphnphichun).Nucho rngccsnphmloi2cchtiuYtrungbnhl10%thvi = 5% cthchpnhn c khng? c) Nu mun c lng t l sn phm loi 2 vi chnh xc nh hn 3% vi tin cy 95% th cn phi kim tra ti thiu bao nhiu sn phm? Cu 6. Kim tra ngu nhin s go bn ra hng ngy mt ca hng, c kt qu: S go bn ra (kg) 120 130 150 160 180 190 210 220 S ngy bn 2 9 12 25 30 20 13 4 a) Ch ca hng cho rng nu trung bnh mi ngy bn ra khng qu 150kg go th tt nht l ngh bn. T s liu trn, vi mc ngha 5% ca hng nn quyt nh th no? b) Nhng ngy bn c trn 200kg l nhng ngy cao im. Hy c lng t l ngy cao im vi tin cy 99%? c) c lng t l ngy cao im vi chnh xc nh hn 5% th tin cy ti a l bao nhiu? d) Gi thit s go bn c trong ngy c phn phi chun v gi go trung bnh l 8000/kg. Vi tin cy 99%, hy c lng trung bnh s tin bn go ca ca hng trong nhng ngy cao im? Cu 7. Kim tra ngu nhin s ko X(kg) bn c hng ngy mt siu th, c kt qu: X (kg)0 5050 100100 150150 200200 250250 300300 350 S ngy923273025205 a)Bngcchthayimubaobvgiygiko,ngitathyskobnctrungbnh trong ngy siu th l 200kg. Vi mc ngha 5%, cho nhn xt v s thay i ny? b) c lng s kotrung bnh bnc trong 1 ngy siu th vi chnh xc nh hn 10kg v tin cy l 97% th cn kim tra ti thiu bao nhiu ngy? c)Nhngngybnctrn250kglnhngngycaoim.Hyclngtlngycao im vi tin cy 88%? d) Gi thit s ko bn c trong ngy c phn phi chun v gi ko trung bnh l 56000/kg. Vi tin cy 99%, hy c lng trung bnh s tin bn ko ca siu th trong nhng ngy cao im? Bi tp Xc Sut Thng K GV L Vn Lai Phin bn 2011 18 Cu 8. Theo di s pht trin chiu cao X(dm) ca cy bch n trng trn t phn sau 1 nm tui, c kt qu: X (dm)25 3030 3535 4040 4545 5050 5555 60 S cy5202530302314 a) Bit chiu cao trung bnh ca bch n sau 1 nm tui t khng c phn l 4,5m. Vi mc ngha 5%, c cn tin hnh khng phn cho bch n khng? b) c c lng chiu cao ca cy bch n trn vi chnh xc nh hn 2dm th m bo tin cy ti a l bao nhiu? c) Nhng cy bch n thp hn 3,5m l cy chm ln. Hy c lng chiu cao trung bnh ca cy bch n chm ln (gi s c phn phi chun) vi tin cy 98%? Cu 9*. nghin cu s pht trin ca 1 loi cy lm giy, ngi ta tin hnh o ngu nhin ng knh X(cm) v chiu cao Y(m) ca mt s cy c bng s liu: Y 234567 X 2035 22210 24381410 264167 28813 a) Nhng cy cao 6m tr ln l cy loi 1. c lng t l cy loi 1 vi tin cy 99%. b) c lng trung bnh v ng knh (gi s c phn phi chun) ca cy loi 1 vi tin cy 98%. c)Trcy,chiucaotrungbnhcaloicynyl5,1m.Sliutrnlynhngcy c p dng k thut chm sc mi. Vi mc ngha 5%, hy cho nhn xt v tc dng ca k thut mi ny? Cu10*.SnphmAchaichtiuchtlnglX(%)vY(kg/mm2).Kimtrangunhin mt s sn phm A, kt qu cho bng sau: Y 0 55 1010 1515 2020 25 X 115 125 7 125 135 12810 135 145 20152 145 155 191695 155 165 83 a) Gi s trung bnh tiu chun ca ch tiu Y l 120kg/mm2, cho nhn xt v sn phm A vi = 5%? b) Sn phm c ch tiu X t 15% tr ln l loi 1 (gi s c phn phi chun). c lng t l v ch tiu X ca sn phm loi 1 vi tin cy 99%? c) c c lng trung bnh ch tiu Y vi chnh xc l 0,6kg/mm2 th m bo tin cy l bao nhiu? Cu 11*. Quan st chiu cao Y(cm) v tui X(nm) ca mt s thanh thiu nin, c bng s liu: Bi tp Xc Sut Thng K GV L Vn Lai Phin bn 2011 19 X 1517192123 Y 145 150 5 150 155 1211 155 160 1486 160 165 1017 165 170 1547 170 17512 a) c lng chiu cao ca nhng ngi 21 tui (gi s c phn phi chun) vi tin cy 99%. b) Nhng ngi cao hn 1,65m l ngi kh cao. c lng t l nhng ngi kh cao vi tin cy 95%? c)Mttiliucnirngchiucaotrungbnhcathanhthiunintrongtuitrnl 153,5cm. Hy cho kt lun v ti liu ny? Cu 12*. Theo di lng phn bn X(kg/ha) vnng sut Y(t/ha)camt loi cy trng trn mt s tha rung (c cng din tch 1 ha), c bng s liu: X 120140160180200 Y 20 2454 24 28 7105 28 32 152012 32 36 796 a) Nng sut di 30 t/ha l nng sut thp. c lng t l cc tha rung c nng sut thp vi tin cy 92%. b) c lng nng sut (gi s c phn phi chun) ca nhng tha rung bn phn 180kg/ha vi tin cy 98%. c) Mt ti liu c ni rng nng sut trung bnh ca loi cy trng ny l 30 t/ha. Vi mc ngha 2%, hy cho kt lun v ti liu ny?