Processing math: 100%

2021年7月25日 星期日

107年專科學力鑑定-初級統計詳解

教育部107年專科學校畢業程度自學進修學力鑑定考試

專業科目(一): 初級統計

解答(10+x+20)÷3=1230+x=36x=6(C)

解答{P(x<63)=P(Z<63754)=P(Z<3)P(X>87)=P(Z>87754)=P(Z>3)P(|Z|>3)10.997=0.003900×0.003=2.7(A)

解答Y=4X6X=14Y+64E(X)=E(14Y+64)=14E(Y)+64=12+32=2(A)

解答E(X)=(1+2+3+4+5+6)÷6=72E(3X)=3E(X)=3×72=212(D)

解答XB(9,12)=np(1p)=9×12×12=32(B)

解答1116×16=136(B)

解答σ(Y)=σ(3X+2)=3σ(X)=3×2=6(C)

解答{B={(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}AB={(6,1),(6,2),(6,3),(6,4),(6,5)}P(AB)=P(AB)P(B)=56(D)

解答ABP(AB)=P(A)P(B)P(AB)=P(AB)P(B)=P(A)P(B)P(B)=P(A)(A)

解答{4=1/245=1/2124×12=125=132(A)

解答{13=1/623=(5/6)(1/6)=5/36P(1X2)=P(X=1)+P(X=2)=16+536=1136(D)

解答P(X<4)=P(X=1)+P(X=2)+P(X=3)=16+16+16=12(C)

解答{:2/5:3/5(,,)2×2×353=12125(,,)32112125×3=36125(D)

解答XB(25,p)EX=np10=25pp=0.4(D)

解答(15%)2=(95%)2=90.25%=0.9025(D)

解答f(x)=3!(3x)!x!×18,x=0,1,2,3P(X1)=P(X=1)+P(X=2)+P(x=3)=f(1)+f(2)+f(3)=18(62+62+66)=18×7=78(C)

解答XPois(λ)P(X=k)=λkeλk!P(X=0)=eλ=e1λ=1E(X)=λ=1E(Y)=E(3X)=3E(X)=3(D)

解答XPois(λ)Var(X)=λ=3E(Y)=E(2X)=2E(X)=2λ=6(B)

解答XPois(λ)E(X)=λ=2P(X=0)=eλ=e2(C)

解答1019{12=110×99=11012=910×19=110110+110=15(B)

解答g(x)g(x)=11000ex1000P(X1000)=100011000ex1000dx=[ex1000]|1000=0+e1(A)

解答E(X)=xf(x)dx=1012xdx=[14x2]|10=14(B)

解答{XN(μx,16)YN(μy,9)Var(XY)=16+9=25σ(XY)=25=5(A)

解答P(Z>1)=0.1587P(Z<1)=10.1587=0.8413P(Z>1)=0.8413P(Z>1)=P(x102>1)=P(x>8)(B)

解答=P(19<x<20)=P(1919.50.5<z<2019.50.5)=P(1<z<1)=P(z<1)+P(z>1)=2P(z>1)=2×0.1587=0.3174(C)

解答(B)

解答()(B)

解答(D)

解答ˉx+zα/2sn=84+1.96×5100=84+0.98=84.98(A)

解答E=zα/2sn=1.645×1.2264=0.25(C)

解答2zα/2p(1p)n=21.96×0.2×0.8100=0.1568(B)

解答μ=zα/2σn{(A)×:σ(B)×:αzα/2(C):n(D)×:(C)

解答E=zα/2σn2.5752n0.7n54.127(A)

解答E=zα/2p(1p)n1.645(1/8)(7/8)n0.04n184.98(D)

解答E=zα/2p(1p)n1.96(120/200)(80/200)200=1.96×350=0.06786.8%(C)

解答n1E21=n2E2270×2.52=n2×1.82n2=135.03(B)

解答z0.025215=z0.005n1.96215=2.575nn=371.09(A)

解答E1n1=E2n20.05×59=0.03×n2n2=163.88(D)

解答=(86.43,93.57)E=(93.5786.43)÷2=3.57=zα/2sn=1.645×15nn=(1.645×15×13.57)2=47.77(A)

解答(A)×::H0H0(C)×:I=:H0H0(D)×:II:HaH0(B)(B)

解答z=20000186003850/30=1.99P(Z>1.99)=0.023P=0.023×2=0.046(D)

解答p=1550=0.3z=0.30.50.5×0.5/50=2.828P(Z>2.828)=1P(Z>2.83)P=P(Z>2.83)=0.0023(B)

解答{P(X>75)=P(Z>75776/n)=P(Z<26/n)=10.004=0.996P(Z>2.65)=0.004P(Z<2.65)=0.99626/n=2.65n=63.2(C)

解答{n1=50,p1=20/50n2=50,p2=30/50{q1=1p1=30/50q2=1p2=20/50s2=p1(1p1)n1+p2(1p2)n2=121250s=0.098z=p2p1s=0.20.098=2.04P(Z>2.04)0.0228(A)

解答{n1=10,ˉx1=8,s1=3n2=10,ˉx2=7,s2=2n3=10,ˉx3=4,s3=1ˉx=(n1ˉx1+n2ˉx2+n3ˉx3)÷(n1+n2+n3)=(80+70+40)÷30=193SSB=n1(ˉx1ˉx)2+n2(ˉx2ˉx)2+n3(ˉx3ˉx)2=10(259+49+499)=2603{32=10i=1(x1iˉx1)210181=x21i(x1i)2/10=x21i802/1022=10i=1(x2iˉx2)210136=x22i(x2i)2/10=x22i702/1012=10i=1(x2iˉx2)21019=x23i(x3i)2/10=x23i402/10{x21i=721x22i=526x23i=169SST=x2ij(xij)2/(n1+n2+n3)=(721+526+169)1902/30=638/3SSW=SSTSSB=(638260)/3=126{MSB=SSB/2=130/3MSW=SSW/27=14/3F=MSB/MSW=130/14=9.28(C)

解答123456Oi89137149Ei101010101010χ2=6i=1(OiEi)2Ei=110(22+12+32+32+42+12)=4(D)

解答:y=5x+50x=55×5+50=75P(X>77)=P(Z>777516)=P(Z>0.5)=0.31(D)

解答b1=r×σ(y)σ(x)=0.6×105=1.2:y=1.2x+60x=10y=1.2×10+60=72(C)

解答{b1xˉxyˉyyˉy=b1(xˉx)y=5(x10)+90x=12y=5(1210)+90=100(A)

解答{b1rR2b1=rσ(y)σ(x)1.4=r105r=0.7=R2R2=0.72=0.49(A)
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