设X~N(1.5,4),求:
(1)P(X﹤3.5);
(2)P(X﹤-4);
(3)P(X﹥2);
(4)P(∣X∣﹤3).
μ=1.5,σ2=4,σ=2. (1)P(X﹤3.5)=Φ[(3.5-1.5)/2]=Φ(1)=0.841 3. (2)P(X﹤-4)=Φ[(-4-1.5)/2]=Φ(-2.75) =1-Φ(2.75)=0.0030. (3)P(x﹥2)=1-P(X≤2)=1-Φ[(2-1.5)/2] =1-Φ(0.25)=1-0.5987 =0.4013. (4)P(∣X∣﹤3)=P(-3﹤X﹤3) =Φ[(3-1.5)/2]-Φ(-3-1.5) =Φ(0.75)-Φ(-2.25) =Φ(0.75)-1+Φ(2.25) =0.7612.