设X~N(3,4)(1)求P{2<X≤5},P{-4<X≤10},P{|X|>2},P{X>3}(2)确定c使得P{X>c}=P{X≤c}

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设X~N(3,4)(1)求P{2<X≤5},P{-4<X≤10},P{|X|>2},P{X>3}(2)确定c使得P{X>c}=P{X≤c}
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设X~N(3,4)(1)求P{2<X≤5},P{-4<X≤10},P{|X|>2},P{X>3}(2)确定c使得P{X>c}=P{X≤c}
设X~N(3,4)(1)求P{2<X≤5},P{-4<X≤10},P{|X|>2},P{X>3}(2)确定c使得P{X>c}=P{X≤c}

设X~N(3,4)(1)求P{2<X≤5},P{-4<X≤10},P{|X|>2},P{X>3}(2)确定c使得P{X>c}=P{X≤c}
N(3,4),则[(x-3)/2]~N(0,1),所以P(2<X≤5)=P(-0.5<[(X-3)/2]≤1)=1-P(x≤-0.5)-P(X>1)=1-0.3085-0.1587=0.5328,P(-4<X≤10)=P(-3.5<[(X-3)/2]≤3.5)≈1,P(|X|>2)=P(X>2)+P(X<-2)=P(X>-0.5)+P(X<-2.5)=0.6915+0.0062=0.6977,P(X>3)=P([(X-3)/2]>0)=0.5,关于第二问,必然是P(X>c)=0.5,因为知道P([(X-3)/2]>0)=0.5,所以c=0×2+3=3