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2021年7月21日 星期三

109年專科學力鑑定-初級統計詳解

教育部109年自學進修專科學校學力鑑定考試

專業科目(一): 初級統計

解答(A)
解答(B)
解答5175:(710)551175C51(710)4×3101(710)5C51(710)4×310=0.47178(B)
解答(B)
解答(C)
解答(B)
解答XP(k,T)=(λT)kk!eλTP(0,T)=eλT1P(0,T)=1eλT{λ=1100T=2001P(0,T)=11e2=10.135=0.8651(99100)200=10.134=0.866(D)
解答p1p115p×1+(1p)×15=80100p=34=75%(D)
解答2+6=89(A)
解答(B)
解答2:423=848=0.5(D)
解答9:(6,36)4(5,46)3(4,56)2(3,6)14+3+2+1=10106×60.278(A)
解答21652(56)5121(56)5=0.598(C)
解答(Coefficient Variance)={A:5/71=0.07B:6/89=0.067C:4/56=0.071B(B)
解答(A)
解答25,25,28,32,33,6034(28+32)÷2=30(B)
解答:ˉx±tα/2sn2×tα/2×sn{n=9s=30tn1=81α=0.95α/2=0.025t:P(t(8)>2.306)=0.025t0.025=2.3062×tα/2×sn=2×2.306×309=46.12(C)
解答n(zα/2)2σ2E2=1.962×30282=54.0225(C)
解答ˉx+zα/2×σn=70+1.645×536=70+1.37=71.37(A):P(Z>1.645)=α/2=0.1/2=0.05zα/2=1.645
解答=2×zα/2×p(1p)n=2×1.96×(10/40)(110/40)40=0.268(D)
解答:XN(μ,σ2)=N(170,42)P(X<166)=P(X1704<1661704)=P(Z<1)=P(Z>1)=0.1587:YN(μ,σ2)=N(164,52)P(Y<166)=P(Y1645<1661645)=P(Z<0.4)=1P(Z>0.4)=10.3446=0.6554nn2166166=n2×0.1587n2×0.1587+n2×0.6554=0.15870.1587+0.6554=0.15870.8141=0.1949(C)
解答{μ=np=50×4%=2σ=np(1p)=50×4%×96%1.386505%=2.5P(X>2.5)=P(Z>2.521.386)=P(Z>0.36)=1P(Z<0.36)=10.6406=0.3594(D)
解答1/23k+2,kZk=0(12)3k+2=122+125+128+=1/2211/23=1/47/8=27=0.2857(C)
解答E=zα/2×p(1p)n=z0.05×2050(12050)50=1.645×0.0690.114=11.4%(C)
解答H0(A)
解答240(Ei)240÷6=40123456Oi254651285535Ei4040404040406i=1(OiEi)2Ei=(152+62+112+122+152+52)÷40=776÷40=19.4(C)
解答dfSSMSFTreatment41=3SSBMSB=55Error204=16SSW=55MSWtotal201=19SST{k=4n=5k=20MSB=55SSW=55MSW=SSW16=5516F=MSBMSW=55×1655=16(A)
解答dfSSMSFTreatment31=2SSBMSB=50Error903=87SSWMSWtotal901=89SST=180{k=3n=30k=90MSB=50SST=180SSB=MSB×2=50×2=100SSW=SSTSSB=180100=80MSW=SSW/87=80/87F=MSB/MSW=50×8780=54.375(D)
解答XYX2Y2XY1010012142204003491612X=7Y=6X2=15Y2=20XY=14r=nXYXYnX2(X)2nY2(Y)2=4×147×64×15724×2062=141144=1422=0.636(C)
解答=+=2%×90%2%×90%+98%×15%=0.109(B)
解答xi=80,35,28,39,75{5i=1xi=2575i=1x2i=15555=x2i15(xi)251=1555(2572)/54=586.3(A)
解答{P(A)=0.6P(B)=0.3P(AB)=0.8P(AB)=P(A)+P(B)P(AB)=0.1(A)×:1P(A)=10.6=0.4P(B)=0.3(B)×:P(A)×P(B)=0.6×0.3=0.18P(AB)=0.1(C):(A)(B):AB(D)×:(C)
解答{P(A)=0.6P(B)=0.3P(AB)=0.2P(AB)=P(A)+P(B)P(AB)=0.7P(AB)=1(P(AB)P(A))=1(0.70.6)=0.9(D)
解答AB=P(AB)=P(A)=0.5(A)
解答ABP(AB)=P(A)×P(B)P(AB)=P(A)+P(B)P(A)×P(B)0.8=0.5+P(B)0.5P(B)0.3=0.5P(B)P(B)=35=0.6(D)
解答σ2(W)=σ2(3X2Y)=32σ2(X)+22σ(Y)232Cov(X,Y)=92+440=34σ(W)=34=5.83(A)
解答=10=1e4×0.5=11e2=10.135=0.865(B)
解答28=r×σ(Y)σ(X)=0.636×nY2(Y)2nX2(X)2=0.636×4×20624×1572=0.636×2=1.272(B)
解答XN(165,42)ˉXN(165,4216)=N(165,1)P(ˉX<163)=P(Z<1631651)=P(Z<2)=P(Z>2)=1P(Z<2)=10.9772=0.0228(D)
解答{P(X=0)=0.25P(X=1)=0.5P(X=2)=0.25E(X)=0×0.25+1×0.5+2×0.25=1E(Y)=E(3X4)=3E(X)4=34=1(C)
解答=C42/C62=0.4=10.4=0.6(B)
解答P(X<163)=P(Z<1631654)=P(Z<0.5)=P(Z>0.5)=1P(Z<0.5)=10.6915=0.3085(C)
解答P(Z<0.25)=0.598760%:Z>0.2540%Z=X28020=0.25X=285(C)
解答(A)×:AB(B)×:{P(A)>0P(B)>0P(AB)=0P(A)P(B)P(AB)AB(C):{B={2,4,6}C={1,2}BC={2}{P(B)=1/2P(C)=1/3P(BC)=1/6P(B)P(C)=16=P(BC)BC(D)×:{A={1,3,5}C={1,2}AC]{1}{P(A)=1/2P(B)=1/3P(AC)=1/6P(A)P(C)=16=P(AC)AC(C)
解答{P(A)=0.5P(AB)=0.2P(AB)=P(A)P(B)P(AB)=0.50.2=0.3=P(A)P(B)=0.5P(B)P(B)=0.6P(AB)=P(A)+P(B)P(AB)=0.5+(10.6)0.2=0.7(D)
解答n(zα/2)2×p(1p)E2=(z0.025)2×1040×(11040)0.052=1.962×316×400=288.12n=289(B)
解答{P(X=1)=0.1P(X=2)=0.2P(X=3)=0.3P(X=4)=0.4{E(X)=1×0.1+2×0.2+3×0.3+4×0.4=3E(X2)=12×0.1+22×0.2+32×0.3+42×0.4=10σ(X)=EX2(EX)2=1032=1σ(Y)=σ(2X2)=2σ(X)=2(A)
解答P(X<20%)=P(Z<0.20.150.2×0.8/200)=P(Z<1.77)=0.962Pvalue=10.962=0.038(B)這題..再想想!!
解答Pvalue=0.015810.0158=0.9842z=2.1574728/n=2.15n=2.15×4=8.6n=8.62=73.96(D)
解答ABC{ABABCP((AB)C)=P(AB)+P(C)P(ABC)=P(A)P(B)+P(C)P(A)P(B)P(C)=0.4(10.2)+0.10.4(10.2)0.1=0.388(C)
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