Answer to Question #264181 in Statistics and Probability for talie

Question #264181

Given the following probabilities, find the value of a if Z ∼ N(0, 1)


(a) P(0 < Z < a) = 0.493


(b) P(−2.5 < Z < a) = 0.5


(c) P(Z < a) = 0.67


(d) P(Z > a) = 0.4025

1
Expert's answer
2021-11-12T04:55:46-0500

for N(0, 1): "\\mu=0,\\sigma=1"

"z=\\frac{x-\\mu}{\\sigma}"


a)

"P(0 < Z < a) =P( Z < a)-P(Z < 0)=P( Z < a)-0.5= 0.493"

"P( Z < a)=0.5+0.493=0.993"

"a=2.455"


b)

"P(-2.5 < Z < a) =P( Z < a)-P(Z <-2.5)=P( Z < a)-0.0062= 0.5"

"P( Z < a)=0.0062+0.5=0.5062"

"a=0.015"


c)

"P(Z < a) = 0.67"

"a=0.44"


d)

"P(Z > a) =1-P(Z < a) = 0.4025"

"P(Z < a)=1-0.4025=0.5975"

"a=0.245"


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