Answer to Question #264178 in Statistics and Probability for talie

Question #264178

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)

1
Expert's answer
2021-11-11T14:07:03-0500

a)


"P(X\\geq500)=1-P(X<500)"

"=1-P(Z<\\dfrac{500-500}{100})=1-P(Z<0)=0.5"

b)


"P(X<300)=P(Z<\\dfrac{300-500}{100})=P(Z<-2)"

"=0.022750"

c)


"P(200\\leq X\\leq800)=P(X\\leq800)-P(X<200)"

"=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(300<X\\leq400)=P(X\\leq400)-P(X\\leq300)"

"=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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