Question

已知智商测验的平均数为100,标准方差为15,随机选取两人,

Answer 1

X~N(100,15^2)

U=X1+X2~N(100,2*15^2)

P(X1+X2>230)=P((U-100)/2^(1/2)*15>(230-100)/2^(1/2)*15)=1-Ф(2^(1/2)=1-0.92=0.08

V=(X1+X2)/2~N(100,(1/4)15^2)

P((X1+X2)/2>115)=P((V-100)/(1/4)15^2>(115-100)/(1/4)15^2)=1-Ф(2)=1-0.97725=0.02275