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

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