Question

Let z denote a variable that has a standard normal distribution. Determine the value z* to satisfy the following conditions. (Round all answers to two decimal places.)
(a) P(z < z*) = 0.0256
z* =
(b) P(z < z*) = 0.0097
z* =  
(c) P(z < z*) = 0.0484
z* =  
(d) P(z > z*) = 0.0204
z* =  
(e) P(z > z*) = 0.0097
z* =  
(f) P(z > z* or z < −z*) = 0.2007
z* =

Answer 1

Solution:

Using standard normal table ,

(a0

P(Z < z) = 0.0256

P(Z < -1.95) = 0.0256

z = -1.95

(b)

P(Z < z) = 0.0097

P(Z < -2.34) = 0.0097

z = -2.34

(c)

P(Z < z) = 0.0484

P(Z < -1.66) = 0.0484

z = -1.66

(d)

P(Z > z) = 0.0204

1 - P(Z < z) = 0.0204

P(Z < z) = 1 - 0.0204

P(Z < 2.05) = 0.9796

z = 2.05

(e)

P(Z > z) = 0.0097

1 - P(Z < z) = 0.0097

P(Z < z) = 1 - 0.0097

P(Z < 2.34) = 0.9903

z = 2.34

(f)

P(z > 1.28 or z < -1.28) = 0.2007