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
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"
Comments
Leave a comment