为自己加油

设X～N(3，2²)，求：
(1)P{2(2)常数c，使P{X﹥C}=P{X≤c}．

(1)∵X～N(3，2²) ∴P{2﹤X≤5} =P{(2-3)/2﹤(X-3)/2≤(5-3)/2) =Φ(1)-Φ(-0.5) =Φ(1)+Φ(0.5)-1=0．5328 P{-4﹤X≤10}=P{(-4-3)/2﹤(X-3)/2<≤(10-3)/2} =Φ(3.5)-Φ(-3.5) =2Φ(3.5)-1=0.9996 P{∣X∣﹥2}=1-P{∣X∣≤2}=1-P{-2≤X≤2} =1-P{-2-3/2≤x-3/2≤(2-3)/2} =1-[Φ(-0．5)-Φ(-2.5)] =Φ(0.5)+1-Φ(2.5)=0．6977 P{X﹥3} =1-P{ X≤3}=1-P{(X-3)/2≤(3-3)/2} =1-Φ(0)=0．5 (2)∵P{X﹥c}=P{X≤c} ∴1-P{X≤c}=P{X≤c} ∴P{X≤c}=1/2 ∴P{(X-2)/2≤(c-3)/2}=Φ[(c-3)/2]=1/2=Φ(0) ∴(c-3)/2=0 ∴c=3