Suppose that X ∼ N(500, 1002), find
(a) P(X ≥ 500)
(b) P(X < 300)
(c) P(200 ≤ X ≤ 800)
(d) P(300 < X ≤ 400)
a)
"=1-P(Z<\\dfrac{500-500}{100})=1-P(Z<0)=0.5"
b)
"=0.022750"
c)
"=P(Z\\leq\\dfrac{800-500}{100})-P(Z<\\dfrac{200-500}{100})"
"=P(Z\\leq 3)-P(Z<-3)"
"=0.9986501-0.0013499=0.997300"
d)
"=P(Z\\leq\\dfrac{400-500}{100})-P(Z\\leq\\dfrac{300-500}{100})"
"=P(Z\\leq -1)-P(Z\\leq-2)"
"=0.1586553-0.0227501=0.135905"
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