已知X~N(2,9),求:(1)P(X≤3);(2)P(X≥1);(3)P(-1≤X≤2)。
解:(1)P(X≤3)=P(X-2/3<3-2/3)=Φ0(1/3)=0.6293 (2)P(X≥1)=1-P(X≤1) =1-P(X-2/3<1-2/3) =1-Φ0(-1/3) =1-(1-Φ0(1/3)) =Φ0(1/3)=0.6293 (3)P(-1≤X≤2)=P(-1-2/3≤X-2/3≤2-2/3) =Φ0(O)-Φ0(-1) =0.5-0.1587 =0.3413
已知X~N(2,9),求:(1)P(X≤3);(2)P(X≥1);(3)P(-1≤X≤2)。
解:(1)P(X≤3)=P(X-2/3<3-2/3)=Φ0(1/3)=0.6293 (2)P(X≥1)=1-P(X≤1) =1-P(X-2/3<1-2/3) =1-Φ0(-1/3) =1-(1-Φ0(1/3)) =Φ0(1/3)=0.6293 (3)P(-1≤X≤2)=P(-1-2/3≤X-2/3≤2-2/3) =Φ0(O)-Φ0(-1) =0.5-0.1587 =0.3413