Question

Find the following z values for the standard normal variable Z. (You may find it useful to reference the z table.Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)

a.	P(Z ≤ z) = 0.1022
b.	P(z ≤ Z ≤ 0) = 0.1641
c.	P(Z > z ) = 0.9719
d.	P(0.29 ≤ Z ≤ z) = 0.3777

Answer 1

Solution :

Using standard normal table,

a)

P(Z z) = 0.1022

P(Z -1.269) = 0.1022

z value = -1.269

b)

P(z Z 0) = 0.1641

P(Z 0) - P(Z z) = 0.1641

0.5 - P(Z z) = 0.1641

P(Z z) = 0.5 - 0.1641 = 0.3359

P(Z -0.424) = 0.3359

z value = -0.424

c)

P(Z > z) = 0.9719

1 - P(Z < z) = 0.9719

P(Z < z) = 1 - 0.9719 = 0.0281

P(Z < -1.909) = 0.0281

z value = -1.909

d) P(0.29 Z z) = 03777

P(Z z) - P(Z 0.29) = 0.3777

P(Z z) = 0.3777 + 0.6141 = 0.9918

P(Z 2.4) = 0.9918

z value = 2.4